I have come back to this question a couple of times now and think I can answer with a couple of suggestions.
I found it hard to imagine punishing a 5 year old child for not being sleepy or letting them cry in their room for a lengthy period of time. Did they punish her as a baby for not going to sleep when they wanted her to go to sleep? Of course not. So why in the world would they assume she is just choosing, in a naughty way, to stay awake. Obviously her 7:30 bedtime is way too early. The fact that she's still awake at 1am and even up to 6am says this is biological and not emotional or a choice she has any control over. So the punishment has to stop.
To me it seems this is not a choice. Seriously, when you are tired can you make yourself stay away for hours and hours, hours and hours? Of course not, your body always wins out and you eventually pass out exhausted.
This child is not doing that in a normal way. She is most likely not producing melatonin or some other chemical that puts us to sleep normally. She needs to see a doc for this.
If this were my child I would have already had her to the doc. If that doc blew me off then I would find another until one listened.
Here are some links about the sleep/awake cycle our bodies go through. It may offer some insight as to what is going on with her body.
http://www.sleepfoundation.org/article/sleep-topics/melat...
http://www.webmd.com/sleep-disorders/tc/melatonin-overview
http://en.wikipedia.org/wiki/Melatonin
This little child is unable to go to sleep on her own, her body is telling itself that it doesn't need it so she never feels sleepy. So by putting her down at 7:30pm they are basically setting themselves up for almost 10 hours of battle each night. A doc needs to do a sleep study on this child and they need to get her treated for this in a medical way so she can start having a better sleep/awake cycle.