A friend reported her phone was constantly being drained, wasn't lasting the day on a full charge and knew how to close apps running in the background (double-click "home" button and hold down app until red minus buttons appear, tap red button)...
I wouldn't usually take notice but I think this is a brilliant example where trying to fix the problem is the very cause of the problem in the first place:
The empty arrow next to the battery indicator tells you that location services is enabled but it is attached to a reminder that needs to constantly monitor your whereabouts in order to "remind you".
The reminder here was to charge the phone but it was the reminder which would drain a full charge in less than a day.