I have found probably a small bug - the app does not quit on Android 4 (S4) even when pressing the Back button (standard Android key). When returning to the menu, it stays loaded. You need to kill the app in the task manager to completely turn it off (usually apps end when the Back button is pressed I think).
I started the game on my phone yesterday, tested it just for something like 2 minutes, and today morning the battery monitoring application says Pyrojump has eaten 11% of the battery and was 15minutes using CPU of which 13minutes was "in the background". Do you use something like NativeApplication.nativeApplication.exit() ? (maybe I am not exact about the function)