If I recall, the radio and interior lights are on the same fuse. It sounds like a possible short in the interior lights, but that SHOULD
blow the fuse, and not work again when the door is closed. What I am thinking is the door opens, it causes a short, and the radio loses power, and then loses it current state.
Hmmmm thinking more, this is even more puzzling, as the radio can lose it's power, and the radio should still maintain its current state and station memory, as there is a constant 12v to the radio that maintains that and the clock. This is a totally different wire from the one the circuit that powers the interior lights and the radio when it is on.
Curious to see what others have to say here.....
[This message has been edited by JohnWPB (edited 01-24-2015).]