iPod Touch does not hold a charge

I had a 3rd generation iPod Touch that would hold a charge for a long time until suddenly (just before the warranty ran out) it would no longer hold the charge. I could fully charge it and leave it sit unused for about 3 days and it would be dead. After much tech support from Apple (we tried restoring original settings, removing all apps, etc., etc., etc.), they sent me a replacement. The replacement has had the same issue since day 1. I have now been experimenting with other settings and it seemed to hold the charge a little better when the wifi was turned off, but I always used to leave the wifi on and it didn't drain the battery at all. What is going on??