Am I doing something to break these iPods?

Just theorizing here, some laptops do not deliver the 500mA the USB standard requires to their USB ports as a power saving technique. Might be that when you first start using it, it manages, but as connectors get a little scuffed up…no more connection.

The slower transfer speed requires that the iPod be in use longer, causing the hard drive to become very hot, and possibly overheat.

Hunh. That sounds at least plausible. Did the iPods stop functioning after particularly long updates?

Given the user name of the OP (percussion) – are you a drummer, by chance? I could see an iPod giving up the ghost if it were in your pocket during a particularly vigourous drum solo.

Shaking and vibration are the enemies of the standard iPod’s hard drive. The iPod nano has no moving parts, which is why my brother recommends it.