Thankfully I don't have, what I would consider, major sleep issues. I can easily go to sleep at night and usually feel refreshed in the morning. My biggest problem is that I relatively regularly wake up in the middle of the night and have a hard time going back to sleep.
It is during the middle of the night that my biggest concerns and fears rear their ugly heads. It is in the middle of the night that I wonder how I am going to deal with all the issues--both big and small--that are going on in my life. It is during the middle of the night that things seem insurmountable.
The wonderful thing about God is that He is always there. He is there first thing in the morning. He is there late at night. He is there in the middle of the night. He is the one person you can really always call without worrying about interfering with anything else He has going on.
When I do wake up in the middle of the night I do my best to continue to turn all my worries and concerns over to God and pray for Him to help me go back to sleep.
Eventually I do go back to sleep and when I wake up in the morning I have a much better perspective on everything. I thank God for that, because I know that my new-found perspective is due to Him.
God is always at work in my life, even in the middle of the night.