Could be a myriad of many things. I agree with Glok, about a physical. Although, if you've been like this your whole life, then it's hard to imagine this not mentioned to a physician and followed up, on?

Some discuss their circadian rhythm. http://www.aasmnet.org/resources/factsheets/crsd.pdf

Personally, having a sleep study, would be my first line of action. An evaluation. From there, once you have definitive answers, you can make your decision about which direction you'd like to treat whatever is leaving you feeling unrestored through any amount of rest.