I need to tear down my mouse because of the middle button that does not respond properly any more. I'd like to try to...

Finally it worked again so I did not had to tear it down... until recently... Now the wheel has become difficult to turn. It is certainly tired... As I'm now decided to replace my mouse, I tried to open it by all means and the good news is that I discovered that the rivet (I mentioned) is a torx screw T6. The bad news is that it's not the only screw, there are two other placed under the front Teflon pad. Then I had to raise the extremities of the pad to access to the screws and I reached not to remove completely the pad.

IMHO, I would say that you effectively got a defective battery. This seems to be the most likely.