user8483: Why do we not remember our past lives?
If it is possible to recollect one's previous lives by deeply concentrated thought,is it not possible for us to visit the hermits living in Himalaya area and verify the truth of doctrine of rebirth?

user8044: There are some persons, who probably in accordance with the laws of association, spontaneously develop the memory of their past birth, and remember fragments of their previous lives. Such cases are very rare, but those few well-attested, respectable cases tend to throw some light on the idea of a past birth for those who doubt the scriptures. Disciples of the Supreme Buddha believe that there are countless past existences. The most valuable evidence Buddhists cite in favour of rebirth is the Buddha, for He developed a knowledge which enabled Him to read past and future lives. Suttas record that prior to Siddhattha Gotama’s Enlightenment, he had gained the three-fold supernormal knowledge. One of which is the rRecollection of his own past lives (pubbenivasanussati-nana). Following His instructions, His disciples also developed this knowledge and were able to read their past lives to a great extent. 
Even some Indian Rishis, before the advent of the Buddha, were distinguished for such psychic powers as clairaudience, clairvoyance, thought-reading, remembering past births, etc. So are the experiences of some modern dependable psychics and strange cases of alternating and multiple personalities. In hypnotic states some relate experiences of their past lives; while a few others, read the past lives of others and even heal diseases.
How are we to account for great characters like Panini, Kalidasa, Homer and Plato; men of genius like Shakespeare, infant prodigies like Pascal, Mozart, Beethoven, Raphael etc.? Heredity alone cannot account for them. "Else their ancestry would disclose it, their posterity, even greater than themselves, demonstrate it." Could they rise to such lofty heights if they had not lived noble lives and gained similar experiences in the past? Is it by mere chance that they are been born or those particular parents and placed under those favourable circumstances? 
A Western writer once said: "Whether we believe in a past existence or not, it forms the only reasonable hypothesis which bridges certain gaps in human knowledge concerning certain facts of every day life. Our reason tells us that this idea of past birth and Kamma alone can explain the degrees of difference that exist between twins, how men like Shakespeare with a very limited experience are able to portray with marvelous exactitude the most diverse types of human character, scenes and so forth of which they could have no actual knowledge, why the work of the genius invariably transcends his experience, the existence of infant precocity, the vast diversity in mind and morals, in brain and physique, in conditions, circumstances and environment observable throughout the world, and so forth." 
It should be stated that this doctrine of rebirth can neither be proved nor disproved experimentally, but it is accepted as an evidentially verifiable fact. The cause of this Kamma is avijja or ignorance of the Four Noble Truths. Ignorance is, therefore, the cause of birth and death; and its transmutation into knowingness or vijja is consequently their cessation. 

user10100: For adults
For adults, they can not remember because it is very far over you can remember it.
Take it easy. Don't look too far, just in this life, you have forgoten everything in your 1-2 years old period already.
For babies
For babies, Take it easy. Just see the  amnesia-patient, it is the same but the reborn is worse than amnesia because reborn-human has an amnesia which is caused by loosen brain, not just damage, also has an amnesia which is caused by psychological trauma, which is caused bad environment in mother's stomach, too. So the babies loose whole of their past life memories.
In very advance theory, abhidhamma, babies can not remember because all of their memory-organs [saññāya āyatana] have change to very weak and none ability, similar to the old paralysis-man's  organs. Also, they have to live in stressful stomach that has 37 °C temperature for at least 7 months, without vision. This is called kammajja-vāta [moving/changing form  that arise by kamma] in suttanta-pāli tradition.
Kammajja-vāta is one element of kammajja-rūpa [form that arise by kamma]. All organs arising at the beginning moment of life, especially human organs, are very weak, loose every ability, walk/see/listen/etc, from the past life.
Mind and it's factors, such as saññā (memory factor), arise depend on those kammajja-rūpa which is a elements of purejāta-paccaya (pre arising cause) in paṭṭhāna, the 7th canon of abhidhamma. If this paccaya, sense-organs, so weak, saññā that arise at these sense-organs also weak too. Then saññā cause of sati (mindfulness, recalling ability mind's factor) by the definition "sati thirasaññāpadaṭṭānā". So the babies loose whole of their past life memories. 
Theravāda recalling skill practice
In theravāda tradition, you can recall it by jhāna-based ñāṇa, such as pupbenivāsānussati-ñāṇa or paccayapariggaha-ñāṇa. This tradition still going on at pa-auk monastery and some Burmese monastery.

user2265: Why do we not remember our past lives?
It is a protective mechanism, kind of like how when you enter REM sleep your body paralyzes you to avoid hurting yourself. Similarly most of our chakras are in a semi-open, unpurified state because the full power of it can be harmful to ourselves and others. Many spiritual powers remain dormant. (I would not rely on the explanations of famous modern teachers because most of them are just intellectuals and have not put the prerequisite solitude and focus to attain realization... and sometimes they have to make publicly acceptable comments to avoid attack.)
If it is possible to recollect one's previous lives by deeply concentrated thought?
Yes. By entering the 1st jhana, one can even recall one's past lives. The below passage from MN 36 indicates Buddha went to 4th jhana before doing so, recalling many more. I would refer to the book Mind Experiment by Bavo Lievens for references on Buddhist texts, as well as beautiful Buddhist cosmology and how to go about doing this. Go to page 80.
Here is an excerpt from MN 36:

"When the mind was thus concentrated, purified, bright, unblemished,
  rid of defilement, pliant, malleable, steady, & attained to
  imperturbability, I directed it to the knowledge of recollecting my
  past lives. I recollected my manifold past lives, i.e., one birth,
  two...five, ten...fifty, a hundred, a thousand, a hundred thousand,
  many eons of cosmic contraction, many eons of cosmic expansion, many
  eons of cosmic contraction & expansion: 'There I had such a name,
  belonged to such a clan, had such an appearance. Such was my food,
  such my experience of pleasure & pain, such the end of my life.
  Passing away from that state, I re-arose there. There too I had such a
  name, belonged to such a clan, had such an appearance. Such was my
  food, such my experience of pleasure & pain, such the end of my life.
  Passing away from that state, I re-arose here.' Thus I remembered my
  manifold past lives in their modes & details."


8483: <p>Why do we not remember our past lives?
If it is possible to recollect one's previous lives by deeply concentrated thought,is it not possible for us to visit the hermits living in Himalaya area and verify the truth of doctrine of rebirth?</p>
 8044: <p>There are some persons, who probably in accordance with the laws of association, spontaneously develop the memory of their past birth, and remember fragments of their previous lives. Such cases are very rare, but those few well-attested, respectable cases tend to throw some light on the idea of a past birth for those who doubt the scriptures. Disciples of the Supreme Buddha believe that there are countless past existences. The most valuable evidence Buddhists cite in favour of rebirth is the Buddha, for He developed a knowledge which enabled Him to read past and future lives. Suttas record that prior to Siddhattha Gotama’s Enlightenment, he had gained the three-fold supernormal knowledge. One of which is the rRecollection of his own past lives (pubbenivasanussati-nana). Following His instructions, His disciples also developed this knowledge and were able to read their past lives to a great extent. </p>

<p>Even some Indian Rishis, before the advent of the Buddha, were distinguished for such psychic powers as clairaudience, clairvoyance, thought-reading, remembering past births, etc. So are the experiences of some modern dependable psychics and strange cases of alternating and multiple personalities. In hypnotic states some relate experiences of their past lives; while a few others, read the past lives of others and even heal diseases.</p>

<p>How are we to account for great characters like Panini, Kalidasa, Homer and Plato; men of genius like Shakespeare, infant prodigies like Pascal, Mozart, Beethoven, Raphael etc.? Heredity alone cannot account for them. "Else their ancestry would disclose it, their posterity, even greater than themselves, demonstrate it." Could they rise to such lofty heights if they had not lived noble lives and gained similar experiences in the past? Is it by mere chance that they are been born or those particular parents and placed under those favourable circumstances? </p>

<p>A Western writer once said: "Whether we believe in a past existence or not, it forms the only reasonable hypothesis which bridges certain gaps in human knowledge concerning certain facts of every day life. Our reason tells us that this idea of past birth and Kamma alone can explain the degrees of difference that exist between twins, how men like Shakespeare with a very limited experience are able to portray with marvelous exactitude the most diverse types of human character, scenes and so forth of which they could have no actual knowledge, why the work of the genius invariably transcends his experience, the existence of infant precocity, the vast diversity in mind and morals, in brain and physique, in conditions, circumstances and environment observable throughout the world, and so forth." </p>

<p>It should be stated that this doctrine of rebirth can neither be proved nor disproved experimentally, but it is accepted as an evidentially verifiable fact. The cause of this Kamma is avijja or ignorance of the Four Noble Truths. Ignorance is, therefore, the cause of birth and death; and its transmutation into knowingness or vijja is consequently their cessation. </p>
 10100: <h2>For adults</h2>

<p>For adults, they can not remember because it is very far over you can remember it.</p>

<p>Take it easy. Don't look too far, just in this life, <strong>you have forgoten everything in your 1-2 years old period already.</strong></p>

<h2>For babies</h2>

<p>For babies, Take it easy. Just see the  <a href="https://en.wikipedia.org/wiki/Amnesia" rel="nofollow noreferrer">amnesia</a>-patient, it is the same but the reborn is worse than amnesia because reborn-human has an amnesia which is caused by loosen brain, not just damage, also has an amnesia which is caused by psychological trauma, which is caused bad environment in mother's stomach, too. <strong>So the babies loose whole of their past life memories.</strong></p>

<p><strong>In very advance theory, abhidhamma</strong>, babies can not remember because all of their memory-organs [saññāya āyatana] have change to very weak and none ability, similar to the old paralysis-man's  organs. Also, they have to live in stressful stomach that has 37 °C temperature for at least 7 months, without vision. <strong>This is called kammajja-vāta [moving/changing form  that arise by kamma] in suttanta-pāli tradition.</strong></p>

<p><strong>Kammajja-vāta</strong> is one element of kammajja-rūpa [form that arise by kamma]. All organs arising at the beginning moment of life, especially human organs, are very weak, loose every ability, walk/see/listen/etc, from the past life.</p>

<p>Mind and it's factors, <strong>such as saññā (memory factor)</strong>, arise depend on those kammajja-rūpa which is a elements of <strong>purejāta-paccaya</strong> (pre arising cause) in paṭṭhāna, the 7th canon of abhidhamma. <strong>If this paccaya, sense-organs, so weak, saññā that arise at these sense-organs also weak too.</strong> Then saññā cause of sati (mindfulness, recalling ability mind's factor) by the definition "sati thirasaññāpadaṭṭānā". <strong>So the babies loose whole of their past life memories.</strong> </p>

<h2>Theravāda recalling skill practice</h2>

<p>In theravāda tradition, you can recall it by <strong>jhāna-based ñāṇa</strong>, such as <strong>pupbenivāsānussati-ñāṇa</strong> or <strong>paccayapariggaha-ñāṇa</strong>. <strong>This tradition still going on at pa-auk monastery and some Burmese monastery.</strong></p>
 2265: <p><strong>Why do we not remember our past lives?</strong></p>

<p>It is a protective mechanism, kind of like how when you enter REM sleep your body paralyzes you to avoid hurting yourself. Similarly most of our chakras are in a semi-open, unpurified state because the full power of it can be harmful to ourselves and others. Many spiritual powers remain dormant. (I would not rely on the explanations of famous modern teachers because most of them are just intellectuals and have not put the prerequisite solitude and focus to attain realization... and sometimes they have to make publicly acceptable comments to avoid attack.)</p>

<p><strong>If it is possible to recollect one's previous lives by deeply concentrated thought?</strong></p>

<p>Yes. By entering the 1st jhana, one can even recall one's past lives. The below passage from MN 36 indicates Buddha went to 4th jhana before doing so, recalling many more. I would refer to the book Mind Experiment by Bavo Lievens for references on Buddhist texts, as well as beautiful Buddhist cosmology and how to go about doing this. Go to page 80.</p>

<p>Here is an excerpt from <a href="http://www.accesstoinsight.org/tipitaka/mn/mn.036.than.html" rel="nofollow">MN 36</a>:</p>

<blockquote>
  <p>"When the mind was thus concentrated, purified, bright, unblemished,
  rid of defilement, pliant, malleable, steady, &amp; attained to
  imperturbability, I directed it to the knowledge of recollecting my
  past lives. I recollected my manifold past lives, i.e., one birth,
  two...five, ten...fifty, a hundred, a thousand, a hundred thousand,
  many eons of cosmic contraction, many eons of cosmic expansion, many
  eons of cosmic contraction &amp; expansion: 'There I had such a name,
  belonged to such a clan, had such an appearance. Such was my food,
  such my experience of pleasure &amp; pain, such the end of my life.
  Passing away from that state, I re-arose there. There too I had such a
  name, belonged to such a clan, had such an appearance. Such was my
  food, such my experience of pleasure &amp; pain, such the end of my life.
  Passing away from that state, I re-arose here.' Thus I remembered my
  manifold past lives in their modes &amp; details."</p>
</blockquote>
