I've seen somewhere that power for the radio is somehow protected by two fuses, and if one of them blows, you get the symptom that the radio does not automatically turns of when you cut the ignition. (probably has something to do with the fact that the radio requires power even when the engine is cut, while the other parts on the same circuit don't).

You should check fuse F10, in the fuse box under the hood (should be a 10A fuse). Perhaps a bad contact, or a flakey fuse? That just may be your culprit ;-) .

Bram