I've had even greater problems with loss of sleep during periods of intense stress and trouble. I remember falling asleep at 2 AM and waking at 4 or 4:30, unable to sleep any longer, dragging myself to work, and repeating the process the following night, and then again the next night, and so on. Sometimes, as I said, it's stress that produces the sleep loss. Other times, it's fear of the future. Other times, it's an unsolvable problem, one that worries me so that I can't get my rest.
However, I realized just a short time ago that I don't need to miss my rest, and that God actually has a plan to help me sleep. It's found in Psalm 3 :
Psalm 3: A psalm of David, when he fled from Absalom his son.
1 LORD, how are they increased that trouble me! many are they that rise up against me.
2 Many there be who say of my soul, "There is no help for him in God."
3 But you, O LORD, are a shield around me; my glory, and the lifter up of my head.
4 I cried to the LORD with my voice, and he heard me out of his holy mountain.
5 I laid myself down and slept; I awoke; for the LORD sustained me.
6 I will not be afraid of ten thousands of people, who have set themselves against me round about.
7 Arise, O LORD; save me, O my God: for you have smitten all my enemies on their cheek bones; you have broken the teeth of the ungodly.
8 Salvation belongs to the LORD: your blessing is upon your people.
It seems like David had a lot of the same troubles I did. He couldn't sleep. He was under intense pressure (more than I have ever been, that's for sure--your own son chasing him with an army, planning to kill him); even his friends were saying, "You're done for, David! God is not going to help you any more!"
But God answered him, and helped him rest and feel refreshed. How? David prayed, remembered that God was his shield and strength, and God strengthened him. Pretty simple, but often disregarded.
It does work. I know. I have fallen asleep many times recently praying, asking God for strength and help, and it arrives with the calming effects of sleep.
There are other strategies, of course: exercise, eating right, not eating too late, not watching television too late (or sometimes, at all), but what seems to have the most effect is that evening call to God for His help--and as He comes to strengthen and comfort, rest arrives with Him, so that when the morning comes, I awake refreshed.
It's really too bad that I took so long to learn this, but I'm passing it on to you so that you can try it as well. It works.
Remember, though, that this is founded on relationship. It's hard to communicate with God unless you have established a relationship with Him. So if this makes little sense to you, it could be that you need to go back to the first step, and that's establishing a relationship with Him as your Father and Lord, and then start with the prayers for His help.
I can't say that He won't help you before you do this because He is good to all, but as your Father, He comes to you personally and meets you wherever you are, and cares for you. If your own human father was not so good, the image of a father isn't going to ring true, and so think of Him then as "The Friend who stays closer than a brother." He is truly the best.