What about where turning it up fixes it? Then it goes back into working. If there were a break, wouldn't it still not work?
With my new stereo I put in a year ago I had the exact same problem. Crutchfield ended up replacing the speakers (the new ones have been flawless), but with the old ones jacking up the volume would at least temporarily fix it. Crutchfield support told me that it was likely a wiring problem, which in my case turned out to be internal to the crossovers in my component speakers. I do know that pulling the new wires through the boot in the front doors was the worst part of the installation and I was afraid I'd stretch something a bit too far and end up having to redo it.
The hard part of a problem like this is that your wires might have just worn somewhere, or maybe your speakers are conking out. If it's neither of those it's your head unit. The only way to find out for sure is to replace them one at a time (wires, speakers, head unit) until the problem goes away. Since the wires are the cheapest, I'd start there. If you're lucky you can use the old wire to pull its replacement through the boot in the door. I'd look at the connections on the speakers first, since that's a lot easier.
