Its because when the battery goes bad the electrolytes solidifies , losing his anti-bounce property.
Link to the video www.youtube.com/watch?v=qrGV7zKEdtU
My chem class did this experiment trying to figure out what it was that makes this happen. I don't remember the results, but we did share our stuff with some science radio show, so that was kind of cool.
Sorry I don't remember the exact details of a high school experiment I didn't care all that much about. Just thought I'd share a relevant story. But good on you for pointing out the flaws in my pointless comment.