The battery on my iPhone 5 is chronic. I charge it through the night, start using it in the morning and the battery is normally totally dead by 7pm if under medium to heavy use.
Is it the phone or IOS6?
I notice whenever I turn it on, the phone starts using it's locating service. The arrow disappears after a couple of seconds, unless I open an app that requires it. My wife has my old iP4 with the latest software, but her battery life is much better.