iPod battery empties over night when iPod is turned off!

When I have charged my iPod to 100% it can play for many hours continuously (10 hours maybe or more). But when I stop playing and turn it off the battery is emty after 1-2 hours (even when it was fully charged).

Can this be a battery problem or is it a problem with the thing inside the iPod that manages the battery consum ???

(I dont really want to spend the money for a new battery which is then maybe again false managed by my iPod and empties as well very rapid when i turn my iPod off ...)

I suppose the reason of the disfunction originates from a electric shock from the car adapter ...

Can anyone help me ?

Thanks :)

Jakob