Vtyjkyuk

I have studied in our texts that a soul will have the memory of its previous births after death, and before birth. My question is when does the soul lose its memory when entering into a body for a birth?

According to the Garbha Upanishad, the soul can remember its past life when it is 9 months old in the womb:

Whatever is consumed or drunk by the mother passes through the nerves
and vessels to the child, becoming the source of his satisfaction.
During the ninth month, all outer signs attain completeness. And he
is reminded of his previous birth, and recounts the good and bad deeds
committed.

This text describes how the foetus is gradually developed over the months in details.

In the 8th month only the foetus gets the status of a full fledged Jiva which is aware of it's own existence.

And from the 9th month onwards, the Jiva contemplates on it's situation. It resolves again and again that if it comes out through that narrow passage of the mother then it will do every possible efforts to make this life it's last life. He resolves thus:

He thinks: I have seen thousands of wombs, eaten several kinds of food
and sucked many breasts. Born and dead again and again, I am immersed
in grief but see no remedy. Thinking of my good and bad deeds, I am
suffering alone, although the bodies that enjoyed the fruits are gone.

When I get out of this womb, I will take refuge in Sā¡khya-Yoga, which
destroys misery and yields liberation; when I get out of this womb, I
will take refuge in Maheśvara, who destroys misery and grants
liberation.

When I get out of this womb, I will take refuge in Nārāyaªa, who
destroys misery and grants liberation. When I get out of this womb, I
will meditate on the eternal Brahman.

But as soon as it comes out of the mother's womb through the passage it forgets all of that, due to the influence of Maya and due to the force of the Suti Vayu:

When he reaches the birth canal and comes out of it with great
difficulty, he is touched by an all-pervading movement [Māyā] that
causes him to forget previous births and the good and the bad deeds
performed therein.

So, as soon as it comes out of the mother's womb --- is the answer.

UPDATE:

The Tantrik compendium ShAtkAnanda Taragini, in it's 1st Chapter, quotes the following verses from Tantras (I'm only giving here the few verses that are relevant to the current topic):

Navame mAsi garbhasthah sarvAn samsmarate hridA |
NavadwAre pure
dehi samayAmshcha vikkArAn ||

During the 9th month [in the womb] the Jiva remembers everything. And,
being situated in the body endowed with the 9 gates, thinks about the
merits and demerits of the Karmas (or conducts).

But, then when it comes out of it's mother's womb, due to pressure and pain of coming out of such a narrow passage, as well as due to the forceful effect of the Suti VAyu, it forgets everything.

Navame dashame mAsi pravalaih suuti mArutaih ||
NihsAryate vAna
iva jantus chidrena sajjvarah |
Patitohapi na jAnAti murchitohapi
tatas chyutim ||
SutivAtasya vegena yonirandhrasya piranAt |

Vismritam jyAnam garbhe yat chintitam hrudi ||
YathA bhavati
tattveshu sutibhuteshu pirnAt |
MAtaram smarati nityam bhubhukshA
drira rodanam ||

And, in the 9th or in the 10th month, the kid, being affected with
severe pain, and by the forceful effect of the Suti VAyu, comes out of
that narrow channel like an arrow. Since it gets immediately
unconscious after coming out of the womb it does not even realise that
it is separated from the mother. Due to the force of the Suti VAyu and
due to the pain and pressure it suffers while coming out of the narrow
passage, it forgets everything - the memory of past life as well all
the reslutions that it had taken. The kid being inflicted by the shaft
like Suti VAyu cries in hunger and always looks for (or remembers)
it's mother.

According to KAlikA PurAna (KP), it's MahAmAyA (the Great Enchantress) who is responsible for all this. We have the following verses here:

GarbhAntarjyAn sampannam preritam suti mArutai |
Utpannam
jyAnarahitam kurute yA nirantaram ||
PurvAti purva samskAra
sammoham samniyojya cha |
AhArArdyau tato moham mamatvam jyAn
samshayam ||
KrodhoparodhanAdishu khsiptvA khsiptvA punah punah
|
PashchAt kAme niyojyAshu chintAtyuktam aharnisham ||

Within the womb the Jiva has full knowledge; but when directed by the
Suti VAyu the Jiva gets born, she (or MahAmAyA) makes it devoid of
that knowledge. And gets it into the SamsAra again and again, which is
full of delusion, compassion, hunger, anger, desires etc etc..

(KP 6- 61,62,53)