I think it's pretty common for most of the iPod products. I know there was a class action suit against Apple that they lost for some of the older iPod batteries prematurely dieing. It's pretty easy to replace them yourself. Go to blueraven.com, I know they sell aftermarket iPod batteries for most of the iPods and they even come with tools and instructions.
I don't have a nano, but mine (2nd Gen 40G) was the same way after a year or two, it would be fully charged on the charger and then I'd take it off and use like 30 minutes later, and it would die.
"Professor, what's another word for pirate treasure?"