Jaap H & SilverCard,
this is bizzare that it could be just a bad batch of batteries. Wonder how many batteries are in this bad batch.
So, I called Apple and opened up a case (don't bother going to the Apple Store, they are of no help). My daugther was going to be using this as an iPod and God forbid if the battery exploded while she had it in her hand or something, the acid would've really harmed her. That's exactly what I Apple Support. They were wonderful in helping me out and understanding the danger.
They were willing to replace it with another iPhone 3GS but that's not what I wanted so they provided me the latest generation (4th) iPod Touch.
I would strongly suggest you call them and open up a case.