My experiences tally with that of the others posting here. I use the Nikon GPS and have it set to stay on all the time the camera is powered up. Thats a real power drain but I can still get nearly a full day shooting(maybe 2-300 exposures) before needing to change batteries.
Sounds like you have a dodgy battery - check the Battery Info on the menus and see what the camera tells you about the condition. If it's new you should have a full set of bars on the Age indicator