user-1: It is commonly known that the Buddha decided that asceticism does not lead to enlightenment, but less common is the reason why given. From Ajahn Brahm's book Mindfulness, Bliss, and Beyond, it appears as though the Buddha abandoned asceticism because eating well was necessary to pursue the jhānas and the Middle Way:

once the Bodhisatta realized that jhāna was the way to enlightenment
  (MN 36,31), he immediately recognized that it was impractical to
  attain jhāna with an emaciated body so began eating well.

Where in MN 36 do we find this reasoning? Is there general agreement in Buddhism that this is indeed why the Buddha decided to give up asceticism?

user7049: here's a precise link to relevant portion of the MN 36
https://suttacentral.net/en/mn36/36-42
the discovery of the middle way is not only manifested in the decision to resume eating and stop tormenting the body because austerities impede entering the jhana, but primarily in my opinion in the actual realization that the pleasure of jhanas is permissible and desirable because it's not sensual, only then came the understanding of incompatibility of severe asceticism with jhanas
this positions the Dhamma halfway between the practices of ascetics who avoided any kind of pleasure, being of the opinion that pleasure in future lives, or even liberation, is secured with suffering in this life (like the jains), and indulgence in low carnal sensuality

user-1: The following findings most directy answer my original question.
An explanation of why the Buddha abandoned asceticism in favor of the Middle Way is given by Bhikku Bodhi in The Noble Eightfold Path -

The other extreme is the practice of self-mortification, the attempt to gain liberation by afflicting the body. This approach may stem from a genuine aspiration for deliverance, but it works within the compass of a wrong assumption that renders the energy expended barren of results. The error is taking the body to be the cause of bondage, when the real source of trouble lies in the mind—the mind obsessed by greed, aversion, and delusion. To rid the mind of these defilements the affliction of the body is not only useless but self-defeating, for it is the impairment of a necessary instrument.
...
Aloof from these two extreme approaches is the Noble Eightfold Path, called the middle way, not in the sense that it effects a compromise between the extremes, but in the sense that it transcends them both by avoiding the errors that each involves. The path avoids the extreme of sense indulgence by its recognition of the futility of desire and its stress on renunciation.
...
But the practice of renunciation does not entail the tormenting of the body. It consists in mental training, and for this the body must be fit, a sturdy support for the inward work. Thus the body is to be looked after well, kept in good health, while the mental faculties are trained to generate the liberating wisdom. That is the middle way, the Noble Eightfold Path, which “gives rise to vision, gives rise to knowledge, and leads to peace, to direct knowledge, to enlightenment, to Nibbāna.”

In MN 53 Sekha Sutta The Disciple in Higher Training, the Buddha emphasizes moderation in eating, and there are at least several other suttas in MN where the Buddha repeats the same.

“And how is a noble disciple moderate in eating? Here, reflecting wisely, a noble disciple takes food...only for the endurance and continuance of this body, for ending discomfort, and for assisting the holy life, considering: ‘Thus I shall terminate old feelings without arousing new feelings and I shall be healthy and blameless and shall live in comfort.’ That is how a noble disciple is moderate in eating.
MN 53 Sekha Sutta The Disciple in Higher Training

Ven. Ayya Khema has repeated this last quote in several of her dhamma talks (for example).
Also thanks to ChrisW for his answer.

user254: Maybe MN 26 is more relevant: towards the end of it, the Five ask questions like,

When this was said, the group of five monks replied to me, 'By that practice, that conduct, that performance of austerities you did not attain any superior human states, any distinction in knowledge & vision worthy of a noble one. So how can you now — living luxuriously, straying from your exertion, backsliding into abundance — have attained any superior human states, any distinction in knowledge & vision worthy of a noble one?'

... and afterwards, the end of the sutta is of their being taught the various jhanas.

There may be somewhere where it's stated as a positive, i.e. "eating well was necessary to pursue the jhānas and the Middle Way" -- I think I've read something like that, but I don't remember whether that's a direct quote or an indirect paraphrase.
The only versions I've found at the moment are expressed as a double-negative, not as a positive, i.e. that "utmost austerity is not the way"; for example from this translation of the (non-canonical) Introduction to the Jâtaka,

And the Future Buddha, thinking, "I will carry austerity to the uttermost," tried various plans, such as living on one sesamum seed or on one grain of rice a day, and even ceased taking nourishment altogether, and moreover rebuffed the gods when they came and attempted to infuse nourishment through the pores of his skin. By this lack of nourishment. his body became emaciated to the last degree, and lost its golden color, and became black, and his thirty-two physical characteristics as a great being became obscured. Now, one day, as he was deep in a trance of suppressed breathing, he was attacked by violent pains, and fell senseless to the ground, at one end of his walking-place.
...
Now the six years which the Great Being thus spent in austerities were like time spent in endeavoring to tie the air 
  into knots. And coming to the decision, "These austerities are not the way to enlightenment," he went begging through villages and market-towns for ordinary material food, and lived upon it. And his thirty-two physical characteristics as a great being again appeared, and the color of his body became like unto gold.
Then the band of five priests thought, "It is now six years that this man has been performing austerities without being able to attain to omniscience. And how much less can he be expected to do so in future, now that he has again taken to ordinary material food begged from town to town! He has become luxurious, and given up the Struggle. For us to look for any benefit to come from that quarter would be as reasonable as if a man were to imagine he could bathe his head in a dew-drop. We will have nothing more to do with him." With that they took their bowls and robes, and left the Great Being, and going eighteen leagues off, entered Isipatana.


There are suttas which describe or recommend an attitude towards food (I expect there are in the vinaya too), for example from the Bhikkhuni Sutta,

'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk, considering it thoughtfully, takes food — not playfully, nor for intoxication, nor for putting on bulk, nor for beautification — but simply for the survival & continuance of this body, for ending its afflictions, for the support of the holy life, [thinking,] 'Thus will I destroy old feelings [of hunger] and not create new feelings [from overeating]. I will maintain myself, be blameless, & live in comfort.' Then he eventually abandons food, having relied on food. 'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said, and in reference to this was it said.


-1: <p>It is commonly known that the Buddha decided that asceticism does not lead to enlightenment, but less common is the reason why given. From Ajahn Brahm's book <a href="https://books.google.com/books?id=ptmMsW16fqkC&amp;lpg=PA129&amp;ots=7HEGKhuTb-&amp;pg=PA129#v=onepage&amp;q&amp;f=false" rel="nofollow">Mindfulness, Bliss, and Beyond</a>, it appears as though the Buddha abandoned asceticism because eating well was necessary to pursue the jhānas and the Middle Way:</p>

<blockquote>
  <p>once the Bodhisatta realized that jhāna was the way to enlightenment
  (MN 36,31), he immediately recognized that it was impractical to
  attain jhāna with an emaciated body so began eating well.</p>
</blockquote>

<p>Where in <a href="https://suttacentral.net/en/mn36" rel="nofollow">MN 36</a> do we find this reasoning? Is there general agreement in Buddhism that this is indeed why the Buddha decided to give up asceticism?</p>
 7049: <p>here's a precise link to relevant portion of the MN 36</p>

<p><a href="https://suttacentral.net/en/mn36/36-42" rel="nofollow">https://suttacentral.net/en/mn36/36-42</a></p>

<p>the discovery of the middle way is not only manifested in the decision to resume eating and stop tormenting the body because austerities impede entering the jhana, but primarily in my opinion in the actual realization that the pleasure of jhanas is permissible and desirable because it's not sensual, only then came the understanding of incompatibility of severe asceticism with jhanas</p>

<p>this positions the Dhamma halfway between the practices of ascetics who avoided any kind of pleasure, being of the opinion that pleasure in future lives, or even liberation, is secured with suffering in this life (<a href="http://www.accesstoinsight.org/tipitaka/mn/mn.014.than.html#pain" rel="nofollow">like the jains</a>), and indulgence in low carnal sensuality</p>
 -1: <p>The following findings most directy answer my original question.</p>
<p>An explanation of why the Buddha abandoned asceticism in favor of the Middle Way is given by Bhikku Bodhi in <a href="https://rads.stackoverflow.com/amzn/click/com/B007626M3E" rel="nofollow noreferrer" rel="nofollow noreferrer">The Noble Eightfold Path</a> -</p>
<blockquote>
<p>The other extreme is the practice of self-mortification, the attempt to gain liberation by afflicting the body. This approach may stem from a genuine aspiration for deliverance, but it works within the compass of a wrong assumption that renders the energy expended barren of results. The error is taking the body to be the cause of bondage, when the real source of trouble lies in the mind—the mind obsessed by greed, aversion, and delusion. To rid the mind of these defilements the affliction of the body is not only useless but self-defeating, for it is the impairment of a necessary instrument.</p>
<p>...</p>
<p>Aloof from these two extreme approaches is the Noble Eightfold Path, called the middle way, not in the sense that it effects a compromise between the extremes, but in the sense that it transcends them both by avoiding the errors that each involves. The path avoids the extreme of sense indulgence by its recognition of the futility of desire and its stress on renunciation.</p>
<p>...</p>
<p>But the practice of renunciation does not entail the tormenting of the body. It consists in mental training, and for this the body must be fit, a sturdy support for the inward work. Thus the body is to be looked after well, kept in good health, while the mental faculties are trained to generate the liberating wisdom. That is the middle way, the Noble Eightfold Path, which “gives rise to vision, gives rise to knowledge, and leads to peace, to direct knowledge, to enlightenment, to Nibbāna.”</p>
</blockquote>
<p>In <em>MN 53 Sekha Sutta The Disciple in Higher Training</em>, the Buddha emphasizes moderation in eating, and there are at least several other suttas in MN where the Buddha repeats the same.</p>
<blockquote>
<p>“And <strong>how is a noble disciple moderate in eating?</strong> Here, reflecting wisely, a noble disciple takes food...only <strong>for the endurance and continuance of this body</strong>, for ending discomfort, and <strong>for assisting the holy life</strong>, considering: ‘Thus I shall terminate old feelings without arousing new feelings and <strong>I shall be healthy and blameless</strong> and shall live in comfort.’ That is how a noble disciple is moderate in eating.</p>
<p>MN 53 Sekha Sutta The Disciple in Higher Training</p>
</blockquote>
<p><a href="http://www.leighb.com/a_khema.htm" rel="nofollow noreferrer">Ven. Ayya Khema</a> has repeated this last quote in several of her dhamma talks (<a href="http://dharmaseed.org/teacher/334/talk/7765" rel="nofollow noreferrer">for example</a>).</p>
<p>Also thanks to ChrisW for <a href="https://buddhism.stackexchange.com/a/17551/8619">his answer</a>.</p>
 254: <p>Maybe <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.026.than.html" rel="nofollow">MN 26</a> is more relevant: towards the end of it, the Five ask questions like,</p>

<blockquote>
  <p>When this was said, the group of five monks replied to me, 'By that practice, that conduct, that performance of austerities you did not attain any superior human states, any distinction in knowledge &amp; vision worthy of a noble one. So how can you now — living luxuriously, straying from your exertion, backsliding into abundance — have attained any superior human states, any distinction in knowledge &amp; vision worthy of a noble one?'</p>
</blockquote>

<p>... and afterwards, the end of the sutta is of their being taught the various jhanas.</p>

<hr>

<p>There may be somewhere where it's stated as a positive, i.e. "eating well was necessary to pursue the jhānas and the Middle Way" -- I think I've read something like that, but I don't remember whether that's a direct quote or an indirect paraphrase.</p>

<p>The only versions I've found at the moment are expressed as a double-negative, not as a positive, i.e. that "utmost austerity is <em>not</em> the way"; for example from this translation of the (non-canonical) <a href="http://www.sacred-texts.com/bud/bits/bits007.htm" rel="nofollow">Introduction to the Jâtaka</a>,</p>

<blockquote>
  <p>And the Future Buddha, thinking, "I will carry austerity to the uttermost," tried various plans, such as living on one sesamum seed or on one grain of rice a day, and even ceased taking nourishment altogether, and moreover rebuffed the gods when they came and attempted to infuse nourishment through the pores of his skin. By this lack of nourishment. his body became emaciated to the last degree, and lost its golden color, and became black, and his thirty-two physical characteristics as a great being became obscured. Now, one day, as he was deep in a trance of suppressed breathing, he was attacked by violent pains, and fell senseless to the ground, at one end of his walking-place.</p>
  
  <p>...</p>
  
  <p>Now the six years which the Great Being thus spent in austerities were like time spent in endeavoring to tie the air 
  into knots. And coming to the decision, "<strong>These austerities are <em>not</em> the way to enlightenment</strong>," he went begging through villages and market-towns for ordinary material food, and lived upon it. And his thirty-two physical characteristics as a great being again appeared, and the color of his body became like unto gold.</p>
  
  <p>Then the band of five priests thought, "It is now six years that this man has been performing austerities without being able to attain to omniscience. And how much less can he be expected to do so in future, now that he has again taken to ordinary material food begged from town to town! He has become luxurious, and given up the Struggle. For us to look for any benefit to come from that quarter would be as reasonable as if a man were to imagine he could bathe his head in a dew-drop. We will have nothing more to do with him." With that they took their bowls and robes, and left the Great Being, and going eighteen leagues off, entered Isipatana.</p>
</blockquote>

<hr>

<p>There are suttas which describe or recommend an attitude towards food (I expect there are in the vinaya too), for example from the <a href="http://www.accesstoinsight.org/tipitaka/an/an04/an04.159.than.html" rel="nofollow">Bhikkhuni Sutta</a>,</p>

<blockquote>
  <p>'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk, considering it thoughtfully, takes food — not playfully, nor for intoxication, nor for putting on bulk, nor for beautification — but simply for the survival &amp; continuance of this body, for ending its afflictions, for the support of the holy life, [thinking,] 'Thus will I destroy old feelings [of hunger] and not create new feelings [from overeating]. I will maintain myself, be blameless, &amp; live in comfort.' Then he eventually abandons food, having relied on food. 'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said, and in reference to this was it said.</p>
</blockquote>
