iPod touch4 battery display issues...replace?

Hi! Well I bought my daughter a 32gb iPod touch 4th generation for 2010 Christmas. By June she had already broken the screen. I took it to the Apple store where they so graciously replaced it...for $150! This iPod has had battery display issues from day 1. According to the display it's almost dead within 30 mins. When I put it on the charger it quickly shows 1/2 full or so. Sometimes it's really at the red line and sometimes the display (warning) has it all wrong. To make a long story short, she's broken the screen again. I've ordered a replacement as well as a new battery. The screen replacement itself is very tedious but the battery requires soddering. Does anyone know if there's another fix for the battery so I can skip the replacement? The software IS up to date. But the battery is crazy and doesn't last long. Also what wouldv'e caused the battery to behave this way? :/

Thanks!