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Praise be to Allah.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) was asked this question, and replied:
If it is three days or less, then he should make up his prayers – by analogy with one who sleeps. If it is more than that then he does not have to make up his prayers – by analogy with one who is insane. And Allaah knows best.