I would try a different source (or use the radio in the receiver) to make sure that it is the problem. Doesn't sound like it is going off due to heat so it could be a bad speaker wire or bad speaker. Check all the speaker wires for possible shorts or bad connections with wires sticking out of the terminals. You can disconnect wires and start by just leaving the center connected and see if it shuts down. If it doesn't connect each speaker one at a time and let it play until you are sure it is OK. When it stops playing that speaker may be at fault.
A good replacement in your price range would be an Onkyo.