iPod Nano Randomly Shuts Off

I've had an iPod Nano 5th generation since late 2010. I started using it mid-2011, and now the iPod randomly shuts off. Even when I think it is turned off, it's still turned on. The battery dies much quicker, and I'm not sure what to do. The closest Apple store is two and a half hours from me, so even if I buy a battery from another store, it is a long drive to an Apple store.