Why was Jesus asleep during the storm?

Sleep signifies spiritual slumber.

His sleeping represents a time when he is with his disciples but they lack active faith. When they fear for their lives, they call upon him with hope. He immediately rebukes them for their lack of faith.

From an intertextuality perspective, I see three relevant passages:

Noah

• survived the deluge enclosed in a floating box
• this becomes the symbol of death and resurrection

Jonah

• Jonah was a prophet
• he was asleep in a boat
• a storm came up
• Jonah is rejected by his own
• Jonah dies and is resurrected
• Jonah goes to the gentiles and they repent

Paul

• Paul was a prisoner on a ship
• a storm destroys the ship
• Paul and all aboard survive

The first two would certainly be known by the author.

It's quite simple. Jesus, being God incarnate, was not bothered by storms (or the problems and trials of life we humans like to lament about) because He has ultimate authority over them and can even use them for His own purposes. The flesh is weak yet the spirit is willing. Suffering is as important as blessings in God's grand narrative. Read the Book of Job and Isaiah 45:7 for more info on this.

Hence why He's sleeping, sarcastically yet silently denouncing the Apostles' embarrassing lack of faith, since they believed they were literally going to die in the storm.

It did not just happen that Jesus was sleeping in the storm. In fact, the storm was too strong and it might have thrown the boat back and forth such that no one would have had the nerve to sleep, yet Jesus was sleeping – certainly, it happened for a good reason. At the end of the story, Jesus calmed the storm and questioned the faith of His disciples. The whole event had happened so that He would teach His disciples to exercise faith in God. Moreover, His disciples learned at firsthand the power of faith. Read the full story here.

Jesus (the man) the same as you and I; would become tired in his human body. Jesus traveled extensively, and he did not have the luxury of any conveyance. Travel was either on foot or aboard an animal such as his entry into Jerusalem on a donkey. Even beyond that Jesus having foreknowledge of his death on a Roman cross; must have had much mental stress.

Matthew 26:38 and 39 KJV  Then saith he unto them, My soul is exceeding sorrowful, even unto death: tarry ye here, and watch with me. And he went a little further, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt.

And the closer he drew to that hour, the greater that stress must have been. In the above Scripture we see that on the night, before his crucifixion; he was distressed to the point that he even asked the Father, if there were another way to save mankind; to please release him from that death. Just imagine that you were aware from birth, that you were going to die a violent death at the hands of some machete wielding thugs. the closer it came to the date the stronger your stress would become. It is a well established medical truth, that great stress is more tiring than physical stress I often thank God that I do not have to suffer as Jesus did, and that he has not shown me the future; or how my demise will occur. I know that in Jesus position I could not be as willing a servant as he was.

It must also be remembered; that Jesus having foreknowledge of his death, would have known they would not perish in the Storm. And that his calming of the storm was for the worry of his compatriots:

Matthew 8:24 through 26 KJV  And, behold, there arose a great tempest in the sea, insomuch that the ship was covered with the waves: but he was asleep. And his disciples came to him, and awoke him, saying, Lord, save us: we perish. And he saith unto them, Why are ye fearful, O ye of little faith? Then he arose, and rebuked the winds and the sea; and there was a great calm. 

His rebuke of them shows that they were not fully believing in his deity.

Hope this helps 

Psalm 107:23-29 (DRB)

They that go down to the sea in ships, doing business in the great waters: 24 These have seen the works of the Lord, and his wonders in the deep. 25 He said the word, and there arose a storm of wind: and the waves thereof were lifted up. 26 They mount up to the heavens, and they go down to the depths: their soul pined away with evils. 27 They were troubled, and reeled like a drunken man; and all their wisdom was swallowed up. 28 And they cried to the Lord in their affliction: and he brought them out of their distresses. 29 And he turned the storm into a breeze: and its waves were still.

Here in the Psalms, God is portrayed as testing His redeemed, by willing there to rise a storm and that they would cry out to Him. I see nothing else here in Matthew 8 than this. We would be 'slow of heart' not to see the intended parallel:

(Ps. 107:25-28)

"there arose a storm of wind: and the waves thereof were lifted up. They mount up to the heavens, and they go down to the depths: their soul pined away with evils."

(Mk. 4:37-38)

"And there arose a great storm of wind, and the waves beat into the ship, so that the ship was filled. 38 And he was in the hinder part of the ship, sleeping upon a pillow; and they awake him, and say to him: Master, doth it not concern thee that we perish?;"

(Ps. 107:28-29)

"and he brought them out of their distresses. 29 And he turned the storm into a breeze: and its waves were still;"

(Mk. 4:39)

"And rising up, he rebuked the wind, and said to the sea: Peace, be still. And the wind ceased: and there was made a great calm."