The fact that they come back on when you restart the system is quite strange. Usually "shorts" will kill your speakers until you fix the loose wire or reattach the wire to the connection. I am thinking this may be your unit. If your speakers work fine, but then die, and after a restart, work again. It sounds like the source is your head unit. You may want to check the wiring at the back of the unit, if that looks fine it could be an internal fault. In which case it is cheaper to get an new one than to fix it.. Have a look at the harness and get back to me.
**Working PART-TIME for Carjunky for a while, Please bare with me =)**