Amazing breaker is a basic 2D game so should last a least 5hrs. The battery needs replacing. Apple will charge $79 for a battery replacement in the US - Apple - Support - Service Answer Center
. It's under repair pricing. If you have an Apple store near by, try that first. Sometimes the Genius' there are really nice and will do a free of charge replacement although if it's out of warranty that's less likely. Remeber
, if it's jailbroken, restore to stock iOS before taking it in. They are more likely to not help you or not give you an offer/deal is it's jailbroken.