I suspect it would take a really long time for the classic band to have this issue, as the connection is metal on metal. If my sport band wears down, they're not so expensive as to prohibit buying a new one, and by that time there will likely be lots of 3rd party bands to choose from.
I've worked out in mine twice, but I haven't done a hard cardio workout in it - I'm waiting for my sport band to arrive before I wear it for seriously sweaty stuff.