If potholes knock them out, there might be an exposed wire somewhere (probably right behind the radio) that is shaking around, and touches bare metal when the car shakes violently.
As for shutting off at high volumes.... that usually happens if the unit gets excessively hot, and shuts itself down for protection. If you touch the front, does it feel warm? If it has a flip-down face plate, flip that down and feel the inner face of it. Excessive heat could be a problem internally with the unit, in which case you need to replace it... or it could be a crossed wire somewhere, causing a short in the speaker outputs. Since you mentioned the pothole thing.... I'm thinking there's bare wire(s) somewhere behind your dashboard, causing both your problems, the random shut downs and the pothole shut downs... and they're getting crossed, either constantly crossed, or intermittently.
Pull your radio out, and check all the wire connections. If you can't find any bare wires or anything that may be shorting out, dig deeper behind the dash. Try pulling the speakers out, and checking the back of them as well.