Strange Issue Please Help

Sorry for the lack of description in the title, but I wasn't sure how to shorten this to title length.

I'm having an issue with my iPhone 4 where about once a day it will randomly stop getting internet, and calls will fail but it says it has 1-2 bars. The battery also drops super fast while this is happening. A simple restart clears up the problem temporarily, usually for the day.

I have tried restores, had my phone replaced by apple, had my sim card replaced, and the only option they are giving me now is to wipe, and restore as a new phone. I REALLY don't want to do that, I have a lot of games and don't want to lose my progress.

So, If anyone has a different suggestion on how to fix it, or a way to restore while backing up just my game saves some how, I would appreciate it.

Thanks for your time!

 

I take it no one has any other ideas?