user19: By far the most popular school of Hindu philosophy, which almost all Hindus nowadays belong to, is the Vedanta school, which is based on an ancient Hindu work called the Brahma Sutras or Vedanta Sutras.  The Brahma Sutras consist of a series of aphorisms which summarize and systematize the philosophical teachings of a set of Hindu scriptures called the Upanishads.  They also spend some time defending the philosophy of the Upanishads against rival schools of Indian philosophy.  In particular, here is what they say concerning Buddhism:

Topic-4: Refutation of Buddhist Realists    

Even if the integration be supposed to arise from either of the causes, that will not be achieved.
If it be argued that a combination becomes possible since (nescience and the rest) can be the causes of one another (in a
  successive series), then we say, no, (for nescience etc.,) can each
  merely be the cause of origin of another just succeeding.
And because the earlier is negated when the later emerges, (therefore nescience and the rest cannot each be the cause of the next
  in the series).
(If it be contended that the effect arises) even when there is no cause, then your assertion (of causation) will be stultified; else (if
  you contend that the entity of the earlier moment continues till the
  entity of the later moment emerges), the cause and effect will exist
  simultaneously.
Neither pratisamkhya-nirodha (artificial annihilation) nor an apratisamkhya-nirodha (natural annihilation) is possible, for there
  can be no cessation (either of the current or of the individuals
  forming the current).
And (the Buddhist view is untenable) owing to defect arising from either point of view.
And (non-existence cannot be asserted) in the case of Akasa on account of the absence of (its) dissimilarity (with destruction).
And (a permanent soul has to be admitted) because of the fact of remembrance (ie., memory).
Something does not come out of nothing, for this does not accord with experience.
And (if something can come out of nothing, then) on the same ground, success should come even to the indifferent people.

Topic-5: Buddhist Idealism Refuted

(External objects are) not non-existent, for they are perceived.
And because of the difference of nature (the waking state is) not (false) like dream etc.
(Tendencies) can have no existence since (according to you) external things are not perceived.
And (the ego-consciousness cannot be the abode), for it is momentary.
Besides (this view stands condemned), it being untenable from every point of view.


My question is, have any Buddhist thinkers responded to this critique of Buddhism? Note that I don't want answerers to try responding to the critique themselves (which might lead to too much speculation and arguments).  I'm just interested in whether any published works have responded to it.
By the way, the aphorisms of the Brahma Sutras are somewhat cryptic, so their meaning and justification are usually understood with the help of commentaries, like this one and this one.
Any help would be greatly appreciated.
Thank You in Advance.
EDIT: Here is a book about the Brahma Sutras' critique of the Vedanta school.

user471: I have not found a single source that addresses the Brahma Sutras directly, but as Bakmoon says, it is possible to find references in texts regarding some of these points. It might be better to add each point or a few relevant points into one question each, with commentaries, in order to obtain good answers.
Points 18 - 21's discussion of cause and effect, seem to be related to and may be answered by SN 12.17 Acela Sutta:
(This comes from here but the full text can be found here)

Again, when the Buddha was asked by the naked ascetic Kassapa whether
  suffering was of one's own making or of another's or both or neither,
  the Buddha replied "Do not put it like that." When asked whether there
  was no suffering or whether the Buddha neither knew nor saw it, the
  Buddha replied that there was, and that he both knew and saw it. He
  then said "Kassapa, if one asserts that 'He who makes (it) feels (it):
  being one existent from the beginning, his suffering is of his own
  making,' then one arrives at eternalism. But if one asserts that one
  makes (it), another feels (it); being one existent crushed out by
  feeling, his suffering is of another's making,' then one arrives at
  annihilationism. Instead of resorting to either extreme a Tathaagata
  teaches the Dhamma by the middle way (by dependent origination)" (S.
  XII, 17/vol. ii, 20).

If Point 25 relates to rebirth as proof that a permanent soul exists in order to transmigrate, then there is an answer here (Milindapanha 3.5.5):

The king asked: "Venerable Nagasena, is it so that one does not
  transmigrate and one is reborn?" "Yes, your majesty, one does
  not transmigrate and one is reborn." "How, venerable Nagasena, is it
  that one does not transmigrate and one is reborn? Give me an analogy."
  "Just as, your majesty, if someone kindled one lamp from another, is
  it indeed so, your majesty, that the lamp would transmigrate from the
  other lamp?" "Certainly not, venerable sir." "Indeed just so, your
  majesty, one does not transmigrate and one is reborn." "Give me
  another analogy." "Do you remember, your majesty, when you were a boy
  learning some verse from a teacher?" "Yes, venerable sir." "Your
  majesty, did this verse transmigrate from the teacher?" "Certainly
  not, venerable sir." "Indeed just so, your majesty, one does not
  transmigrate and one is reborn."

There is a discussion on the above in another answer. That compares the discovery of quantum entanglement in physics, with the above.
However, if Point 25 relates to memory in our present lifetime as suggested by this Brahma Sutras' commentary, then I would say that when a person experiences brain damage, he could lose his memories (from a modern day scientific perspective). So, if having memories is proof of having a permanent soul that links them together, then is losing one's memories proof of losing one's soul? This can be linked to the following quote:

The characteristic is stated more succinctly in this way: "The eye
  (ear, nose, tongue, body, and mind, and six external bases) is
  impermanent; what is impermanent is suffering; what is suffering is
  not self" (S. XXXV, 1/vol. iv, 1); or "All is not-self. And what is
  the all that is not self? The eye is not self..." (S. XXXV, 45/vol.
  iv, 28); or again "All things (dhamma) are not-self" (e.g. Dh. XX,
  7/v. 279). The canonical commentary, the Pa.tisambhidaamagga, adds
  "Materiality (etc.) is not-self in the sense that it has no core
  (saara)" (Ps. ~Naanakathaa/vol. i, 37).


user13146: Here is the list of the Buddhist and Hindu Acaryas in chronological order based on their dates and who critiqued whom. 

Nāgārjuna(1st C.E) critiqued by Vātsyāyana (400 C.E)
Vātsyāyana critiqued by Dignāga(500 C.E)
Dignāga critiqued by Kumārila bhaṭṭa/Saṇkarācarya(6th-7th century)
Kumarila bhatta/Saṇkarācarya critiqued by Dharmakriti (6th or 7th century)
Dharmakriti critiqued by Vācaspati Miśra(841 C.E)
Vācaspati Miśra critiqued by Jñānaśrimitra(975-1025 C.E)
Jñānaśrimitra ( C.E) critiqued by (C.E) Udayanācārya (10th -11th century)
Udayanācārya( C.E) critiqued by Ratnakirti(C.E)
Ratnakirti (11th century CE) critiqued by none so far.

So, yes of course the Vedanta/hindu philosophy propounded in Brahma Sutra is critiqued by Buddhist philosophers time and again in the history of development of Indian philosophy. 
As you might have been familiar with the style of the Indian philosophers, they did not critique the texta per se but the tenent systems in them. 

user43: I think Nagarjuna's Mulamadhyamakakarika is the work you are looking for. Just like Brahma-sutras does not mention specific Buddhist sutras it debates with, Mulamadhyamakakarika does not mention Brahma-sutras, but it does methodically address the same points.
As ancient texts go, Mulamadhyamakakarika is way too obscure to be brought in here and contrasted point by point, luckily the details of the polemics between the two commentary traditions are surveyed in the book you mentioned, a modern (1980s) work "An Evaluation of the Vedantic Critique of Buddhism". The author concludes (emphasis mine):

In this work, an attempt has been made to compare the interpretations by Shankara, Ramanuja, and Madhva of those sutras of the Vedantic texts, the Brahma-sutra, devoted to a refutation of Buddhism. An attempt has also been made to compare the interpretation by each Vedantic commentator of a particular Buddhist school's position with the actual Buddhist school's position as set forth in its own texts. It has been discovered that Buddhist positions were often distorted out of ignorance or deliberate intent, and that the Vedantic commentators proceeded to build their refutations of Buddhism on the basis of incorrect assumptions. It may have been the case that other matters were of more pressing concerns to the Vedantic commentators than the refutation of Buddhism. [...] In any case, however, it may be concluded that Buddhist positions have not been portrayed correctly in the Vedantic commentaries to the Brahma-sutra.

Another work that compares and contrasts Vedanta and Buddhism is Acharya Mahayogi Sridhar Rana Rinpoche's essay "Madhyamika Buddhism vis-à-vis Hindu Vedanta". Instead of debating with Brahma-sutras it addresses Swami Vivekananda's claim that Buddhism was an offshoot of Vedanta. Although it does not directly address your question, the essay is very informative if you are interested in comparative studies:

In conclusion, I would like to sum it up by stating that Buddhism (especially Mahayana/Vajrayana) is not a reformulation of Hinduism or a negative way of expressing what Hinduism has formulated positively. Hinduism and Buddhism share a common cultural matrix and therefore tend to use the same or similar words. Even though they share certain concepts like karma and re-incarnation, their interpretations differ. Hindu concepts of karma and reincarnation tend to be rather linear, whereas the Buddhist concept is linked with pratityasamutpada. [...] However, all similarities to Hinduism end there. The Shunyata of the Buddha, Nagarjuna and Candrakirti is by no means a negative way of describing the Brahman of the Upanishad, Samkara and Vidhyaranya groups.


19: <p>By far the most popular school of Hindu philosophy, which almost all Hindus nowadays belong to, is the <a href="http://en.wikipedia.org/wiki/Vedanta">Vedanta</a> school, which is based on an ancient Hindu work called the Brahma Sutras or Vedanta Sutras.  The Brahma Sutras consist of a series of aphorisms which summarize and systematize the philosophical teachings of a set of Hindu scriptures called the Upanishads.  They also spend some time defending the philosophy of the Upanishads against rival schools of Indian philosophy.  In particular, <a href="http://www.advaita.it/library/brahmasutras2.htm">here</a> is what they say concerning Buddhism:</p>

<blockquote>
  <p>Topic-4: Refutation of Buddhist Realists    </p>
  
  <ol start="18">
  <li>Even if the integration be supposed to arise from either of the causes, that will not be achieved.</li>
  <li>If it be argued that a combination becomes possible since (nescience and the rest) can be the causes of one another (in a
  successive series), then we say, no, (for nescience etc.,) can each
  merely be the cause of origin of another just succeeding.</li>
  <li>And because the earlier is negated when the later emerges, (therefore nescience and the rest cannot each be the cause of the next
  in the series).</li>
  <li>(If it be contended that the effect arises) even when there is no cause, then your assertion (of causation) will be stultified; else (if
  you contend that the entity of the earlier moment continues till the
  entity of the later moment emerges), the cause and effect will exist
  simultaneously.</li>
  <li>Neither pratisamkhya-nirodha (artificial annihilation) nor an apratisamkhya-nirodha (natural annihilation) is possible, for there
  can be no cessation (either of the current or of the individuals
  forming the current).</li>
  <li>And (the Buddhist view is untenable) owing to defect arising from either point of view.</li>
  <li>And (non-existence cannot be asserted) in the case of Akasa on account of the absence of (its) dissimilarity (with destruction).</li>
  <li>And (a permanent soul has to be admitted) because of the fact of remembrance (ie., memory).</li>
  <li>Something does not come out of nothing, for this does not accord with experience.</li>
  <li>And (if something can come out of nothing, then) on the same ground, success should come even to the indifferent people.</li>
  </ol>
  
  <p>Topic-5: Buddhist Idealism Refuted</p>
  
  <ol start="28">
  <li>(External objects are) not non-existent, for they are perceived.</li>
  <li>And because of the difference of nature (the waking state is) not (false) like dream etc.</li>
  <li>(Tendencies) can have no existence since (according to you) external things are not perceived.</li>
  <li>And (the ego-consciousness cannot be the abode), for it is momentary.</li>
  <li>Besides (this view stands condemned), it being untenable from every point of view.</li>
  </ol>
</blockquote>

<p>My question is, have any Buddhist thinkers responded to this critique of Buddhism? Note that I don't want answerers to try responding to the critique themselves (which might lead to too much speculation and arguments).  I'm just interested in whether any published works have responded to it.</p>

<p>By the way, the aphorisms of the Brahma Sutras are somewhat cryptic, so their meaning and justification are usually understood with the help of commentaries, like <a href="http://www.sacred-texts.com/hin/sbe34/index.htm">this one</a> and <a href="http://www.sacred-texts.com/hin/sbe48/index.htm">this one</a>.</p>

<p>Any help would be greatly appreciated.</p>

<p>Thank You in Advance.</p>

<p>EDIT: <a href="https://books.google.com/books?id=ARxOBD6m8EIC&amp;source=gbs_navlinks_s">Here</a> is a book about the Brahma Sutras' critique of the Vedanta school.</p>
 471: <p>I have not found a single source that addresses the Brahma Sutras directly, but as Bakmoon says, it is possible to find references in texts regarding some of these points. It might be better to add each point or a few relevant points into one question each, with commentaries, in order to obtain good answers.</p>

<p>Points 18 - 21's discussion of cause and effect, seem to be related to and may be answered by SN 12.17 Acela Sutta:
(This comes from <a href="http://www.accesstoinsight.org/lib/authors/various/wheel202.html#theravada" rel="nofollow noreferrer">here</a> but the full text can be found <a href="http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.017.than.html" rel="nofollow noreferrer">here</a>)</p>

<blockquote>
  <p>Again, when the Buddha was asked by the naked ascetic Kassapa whether
  suffering was of one's own making or of another's or both or neither,
  the Buddha replied "Do not put it like that." When asked whether there
  was no suffering or whether the Buddha neither knew nor saw it, the
  Buddha replied that there was, and that he both knew and saw it. He
  then said "Kassapa, if one asserts that 'He who makes (it) feels (it):
  being one existent from the beginning, his suffering is of his own
  making,' then one arrives at eternalism. But if one asserts that one
  makes (it), another feels (it); being one existent crushed out by
  feeling, his suffering is of another's making,' then one arrives at
  annihilationism. Instead of resorting to either extreme a Tathaagata
  teaches the Dhamma by the middle way (by <a href="https://buddhism.stackexchange.com/q/48/471">dependent origination</a>)" (S.
  XII, 17/vol. ii, 20).</p>
</blockquote>

<p>If Point 25 relates to rebirth as proof that a permanent soul exists in order to transmigrate, then there is an answer <a href="http://www.accesstoinsight.org/tipitaka/kn/miln/miln.3x.kell.html#miln" rel="nofollow noreferrer">here</a> (Milindapanha 3.5.5):</p>

<blockquote>
  <p>The king asked: "Venerable Nagasena, is it so that one does not
  transmigrate and one is reborn?" "Yes, your majesty, one does
  not transmigrate and one is reborn." "How, venerable Nagasena, is it
  that one does not transmigrate and one is reborn? Give me an analogy."
  "Just as, your majesty, if someone kindled one lamp from another, is
  it indeed so, your majesty, that the lamp would transmigrate from the
  other lamp?" "Certainly not, venerable sir." "Indeed just so, your
  majesty, one does not transmigrate and one is reborn." "Give me
  another analogy." "Do you remember, your majesty, when you were a boy
  learning some verse from a teacher?" "Yes, venerable sir." "Your
  majesty, did this verse transmigrate from the teacher?" "Certainly
  not, venerable sir." "Indeed just so, your majesty, one does not
  transmigrate and one is reborn."</p>
</blockquote>

<p>There is a discussion on the above in <a href="https://buddhism.stackexchange.com/a/7539/471">another answer</a>. That compares the discovery of quantum entanglement in physics, with the above.</p>

<p>However, if Point 25 relates to memory in our present lifetime as suggested by this Brahma Sutras' <a href="http://www.swami-krishnananda.org/bs_2/bs_2-2-04.html" rel="nofollow noreferrer">commentary</a>, then I would say that when a person experiences brain damage, he could lose his memories (from a modern day scientific perspective). So, if having memories is proof of having a permanent soul that links them together, then is losing one's memories proof of losing one's soul? This can be linked to the following <a href="http://www.accesstoinsight.org/lib/authors/various/wheel202.html#theravada" rel="nofollow noreferrer">quote</a>:</p>

<blockquote>
  <p>The characteristic is stated more succinctly in this way: "The eye
  (ear, nose, tongue, body, and mind, and six external bases) is
  impermanent; what is impermanent is suffering; what is suffering is
  not self" (S. XXXV, 1/vol. iv, 1); or "All is not-self. And what is
  the all that is not self? The eye is not self..." (S. XXXV, 45/vol.
  iv, 28); or again "All things (dhamma) are not-self" (e.g. Dh. XX,
  7/v. 279). The canonical commentary, the Pa.tisambhidaamagga, adds
  "Materiality (etc.) is not-self in the sense that it has no core
  (saara)" (Ps. ~Naanakathaa/vol. i, 37).</p>
</blockquote>
 13146: <p>Here is the list of the Buddhist and Hindu Acaryas in chronological order based on their dates and who critiqued whom. </p>

<ul>
<li>Nāgārjuna(1st C.E) critiqued by Vātsyāyana (400 C.E)</li>
<li>Vātsyāyana critiqued by Dignāga(500 C.E)</li>
<li>Dignāga critiqued by Kumārila bhaṭṭa/Saṇkarācarya(6th-7th century)</li>
<li>Kumarila bhatta/Saṇkarācarya critiqued by Dharmakriti (6th or 7th century)</li>
<li>Dharmakriti critiqued by Vācaspati Miśra(841 C.E)</li>
<li>Vācaspati Miśra critiqued by Jñānaśrimitra(975-1025 C.E)</li>
<li>Jñānaśrimitra ( C.E) critiqued by (C.E) Udayanācārya (10th -11th century)</li>
<li>Udayanācārya( C.E) critiqued by Ratnakirti(C.E)</li>
<li>Ratnakirti (11th century CE) critiqued by none so far.</li>
</ul>

<p>So, yes of course the Vedanta/hindu philosophy propounded in Brahma Sutra is critiqued by Buddhist philosophers time and again in the history of development of Indian philosophy. </p>

<p>As you might have been familiar with the style of the Indian philosophers, they did not critique the texta per se but the tenent systems in them. </p>
 43: <p>I think Nagarjuna's <a href="https://en.wikipedia.org/wiki/M%C5%ABlamadhyamakak%C4%81rik%C4%81" rel="noreferrer">Mulamadhyamakakarika</a> is the work you are looking for. Just like Brahma-sutras does not mention specific Buddhist sutras it debates with, Mulamadhyamakakarika does not mention Brahma-sutras, but it does methodically address the same points.</p>

<p>As ancient texts go, Mulamadhyamakakarika is way too obscure to be brought in here and contrasted point by point, luckily the details of the polemics between the two commentary traditions are surveyed in the book you mentioned, a modern (1980s) work "<a href="http://rads.stackoverflow.com/amzn/click/8120803639" rel="noreferrer">An Evaluation of the Vedantic Critique of Buddhism</a>". The author concludes (emphasis mine):</p>

<blockquote>
  <p>In this work, an attempt has been made to compare the interpretations by Shankara, Ramanuja, and Madhva of those sutras of the Vedantic texts, the Brahma-sutra, devoted to a refutation of Buddhism. An attempt has also been made to compare the interpretation by each Vedantic commentator of a particular Buddhist school's position with the actual Buddhist school's position as set forth in its own texts. <strong>It has been discovered that Buddhist positions were often distorted out of ignorance or deliberate intent, and that the Vedantic commentators proceeded to build their refutations of Buddhism on the basis of incorrect assumptions.</strong> It may have been the case that other matters were of more pressing concerns to the Vedantic commentators than the refutation of Buddhism. [...] <strong>In any case, however, it may be concluded that Buddhist positions have not been portrayed correctly in the Vedantic commentaries to the Brahma-sutra.</strong></p>
</blockquote>

<p>Another work that compares and contrasts Vedanta and Buddhism is Acharya Mahayogi Sridhar Rana Rinpoche's essay "<a href="http://buddhism.lib.ntu.edu.tw/FULLTEXT/JR-BH/bh117532.htm" rel="noreferrer">Madhyamika Buddhism vis-à-vis Hindu Vedanta</a>". Instead of debating with Brahma-sutras it addresses Swami Vivekananda's claim that Buddhism was an offshoot of Vedanta. Although it does not directly address your question, the essay is very informative if you are interested in comparative studies:</p>

<blockquote>
  <p>In conclusion, I would like to sum it up by stating that Buddhism (especially Mahayana/Vajrayana) is not a reformulation of Hinduism or a negative way of expressing what Hinduism has formulated positively. Hinduism and Buddhism share a common cultural matrix and therefore tend to use the same or similar words. Even though they share certain concepts like karma and re-incarnation, their interpretations differ. Hindu concepts of karma and reincarnation tend to be rather linear, whereas the Buddhist concept is linked with pratityasamutpada. [...] However, all similarities to Hinduism end there. The Shunyata of the Buddha, Nagarjuna and Candrakirti is by no means a negative way of describing the Brahman of the Upanishad, Samkara and Vidhyaranya groups.</p>
</blockquote>
