I have an iPhone4 around a year old running iOS 4.3.3.
I don't know when this problem started... I usually charge before hitting 30% battery. Of course the one time I need to use the phone for an emergency and don't have a charger handy I have a problem
At 29% battery the phone will shut itself off and show the charge screen. If I do a hard reset the phone will come on... boot up... then turn itself off again.
If I charge the phone to 30-31% it will work perfectly fine until it hits 29%. I've repeated this a dozen times to make sure.
I've tried everything I can think of to try to fix this problem. I can't really find anyone else with the exact same problem.