Ignition sense maybe?
Hmmm. What happens (on an unaffected player) if you turn off the ignition, turn the player back on, turn the ignition back on, and turn the ignition off again? Does it stay awake that time or does it turn ``off''?

If it turns off, I can see that it might well be the ignition line. Do you have a multimeter to check it? But, I forget, didn't someone say they saw this on AC power, too?
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Bitt Faulk