If a person is very sleepy while praying, for example, he can barely stand or keep his eyes open, he keeps forgetting or does not know at which point of the prayer in which he is, he doesn't know that which he is saying, etc., then can he take a nap, even if he thinks that he will most likely miss the time of the prayer, and then perform it later? Especially at thuhr and 'ishaa.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, is His slave and Messenger.

If the prayer during which the worshipper felt drowsy or fears to have felt drowsy is a voluntary prayer, then it is permissible to sleep without performing it and there is no problem in this regard. This is evidenced by the Hadeeth that reads: “If one of you feels drowsy while performing a prayer, he should lie down until his slumber has gone away, because if one performs the prayer while drowsy, he does not know (if he prays in such a state) he might insult himself (by mistake) instead of asking for forgiveness.” [Al-Bukhari, Maalik, and others]

If he feels drowsy while performing an obligatory prayer, yet he is able to perform the pillars of the prayer and is mindful of what he is saying, then he should perform the prayer and not delay it beyond its due time. However, if he is unable to do so, he should consider whether or not it is possible to delay the prayer and perform it before its due time ends. If there is no adequate time, Muslim jurists stated that he should, in the first place, diligently fight off drowsiness and perform the prayer instead of sleeping and delaying it. He should, then, make up for this prayer after waking up if he doubts whether it was performed in a way that fully clears his liability of the obligation. Abu Al-Waleed Al-Baaji, said in Al-Muntaqa, commenting on the Hadeeth: “His statement, ‘because if one performs the prayer while drowsy, he does not know (if he prays in such a state) he might insult himself instead of asking for forgiveness,’ means that if a person performs a prayer in a state of drowsiness, he will not be sure whether or not he is asking for forgiveness and may even end up cursing himself instead of asking for forgiveness, and this contradicts the essence of the prayer. The word ‘prayer’ was used in the Hadeeth as a general term to refer to any given prayer. However, Imam Maalik held that it refers to night prayers, and this opinion was held by a group of scholars because overwhelming sleep often occurs at the time of the night prayer.

If this occurred while performing an obligatory prayer and there is enough time to (rest for a while to) overcome drowsiness and then perform the prayer before its time expires or that someone would wake him up to perform the prayer (at a later time) before its time ends, he may sleep and prepare to perform the prayer later on, within its due time. However, if there is insufficient time and he knows that sleeping would result in missing the prayer, he should perform the prayer to the best of his ability, strive to perform it in a correct way, and then go to sleep. If he knows with certainty that he performed the pillars and the obligatory acts of the prayer, so be it; otherwise, he should make up for it after waking up from sleep.” [End of Quote]

Allah knows best.