I hardly ever get a good night's sleep! I wake up in the early hours and feel quite 'muzzy' so need to do a blood test. It's usually okay and the weird feeling is because I've just woken from a deep sleep, but it's hard to tell when I'm in that state! I think I get quite anxious about having a hypo while I sleep, so it's always there at the back of my mind. Do you find it's your actual sugar levels or the worry of what they might be that keeps you awake?
Diabetics are prone to sleep apnea and in fact sleep apnea can actually cause diabetes. Now this may not be what you have, but seeing a doctor and asking him about your condition and possibly conducting a sleep exam could let you know what's going on in short order, or at the very least rule out something serious.
This brings up a very interesting point about sleep deprivation, but I'll post this in a new thread.