Same question as pushrod. Does this happen with the key removed? There is a switch to disable the dome lights, but with the key off and the driver door open, nothing else should stay on at all. If the key is removed and the driver door open and the radio is still on, you have a problem. Could be the door ajar input switch, could be the BCM, could be the RAP module, or could be wiring in any of the circuits to those parts.
It stays on with the key removed. I think I found the switch it is somehow connected with the door latch. When I got it to act up I manually threw the latch closed and opened it with the inside handle. That would trigger it and shut the radio off. I sprayed PB Blaster in the latch to lube it and it has been fine since.