There are two possible views of why Jesus did not wake up during the storm at sea:
Jesus was sleeping in the stern of the boat (Mark 4:38), because, in his true human nature, he was exhausted after a long day of preaching and performing miracles.
Jesus withdrew himself from his disciples both to give himself much needed rest and to give his disciples the opportunity to demonstrate their weak faith and his power to save despite that weak faith
Interpretation 1:
Despite the waves swamping the boat, Jesus lay asleep in the stern (Mark 4:38). Here we see evidence that Jesus was truly man, for he was tremendously tired after a long day.1
Interpretation 2:
In and of itself it is of course fully understandable that Jesus, having endured so much prior, would now fall into such a deep sleep, that not even the great storm would wake him. Nonetheless, it is important to see the nap which he took as itself a positive action, for he thereby purposefully withdrew himself from his disciples so that they themselves could see the weakness of their own faith.2
24 Et voici, il s'éleva sur la mer une si grande tempête que la barque était couverte par les flots. Et lui, il dormait.