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If you can't turn it on or it shuts off when you hit a bump it may be the on/off -volume pot. Obsolete part but you can remove and clean with radio cleaner- deoxit is the brand that works good. I shot a little down the stem, let it soak in, then turn it on/off several times and it worked. I should remove the pot and carefully open it up to clean it with the deoxit.
You can check the wiring connector but I suspect that is ok since you can turn in back on.
IF -it's an aftermarket radio....educated guess...
You have a bad speaker - a shorting voice coil. The radio's output heats up and the protection circuit come on shut down the audio amp section- radio will stay lit but no sound.
When you turn the **** off and on it'll reset the protection circuit.