When you say "She's not getting enough sleep", what do you mean by that? Is your meaning limited to "She's not getting the recommended/customary about of sleep", or is there any impact on her personality or behavior since this started?
Have you talked to her to ask her if there's some reason she doesn't want to sleep? Can she explain what's going on in her head when she's lying in bed awake? She's not a neurologist but kids can be surprisingly good at coming up with metaphors for how they're feeling.
When she's awake, if you try to leave her alone, is she constantly bothering you, or will she sit in her room quietly and read / draw / play with stuffed animals or something else? How does she feel about being awake -- is she happy, frustrated, desperate?
When I was that age I would intermittently be awake until 2am, 3am or later. I described it to my parents as my brain running and running and not wanting to calm down. They suggested several mental relaxation exercises -- those relaxed me but didn't help me sleep. Eventually we found out it was a food sensitivity -- certain foods prevent my brain from damping down its own excitement (the daytime symptom was hyperactivity). Adjusting my diet solved both the hyperactivity and the insomnia.
Standard disclaimer: Your daughter is different than me; her problem is probably not the same as mine; diet-induced hyperactivity and insomnia is rare.
EDIT: I didn't include this anecdote to suggest a solution to the problem; I included it to show that (a) there is probably some physical reason for it--she isn't just "being difficult"; (b) it's going to be hard to find out what that reason is; (c) she probably has some inkling as to what's wrong but can't express it; (d) this probably won't damage or even affect her at all in the longterm; (e) show you care and don't get overly upset about it -- be available within reason but don't overexert yourself.
