
As an alternative to sending your iPod Touch to Apple where it would be replaced with a different unit, causing you to lose any media or software on it, you can send it to a company called Milliamp Ltd instead. Milliamp's technicians will install a replacement battery that they guarantee for 10 years, and now they'll even get it done in a day. The best part is the price, which is about 3/4 what Apple would charge you.
As an option you can simply order the battery to replace it yourself, but Milliamp won't provide any instructions or support so it's not recommended unless you have a lot of confidence that you know what you're doing.
You can find more information on Milliamp's website.