My idea is probably flawed. The only way that I think this could really be the problem is if at the penultimate shutdown the player was in standby. I guess this is feasible, especially if the player is used at home a lot too:

1) On AC power. Player put into standby because it's bedtime. Screen turns off.
2) Player pulled from dock whilst still in standby. Flash saves correctly.
3) Player inserted into car, gets correct settings (including expected standby).
4) Player brought out of standyby and used. Then pulled, whilst screen is busy and disks spun up. Flash not written correctly.
5) Player inserted - settings are obtained from the AC save again.

Of course, low voltage in the car would probably exacerbate this problem - the power during shutdown is coming from the empeg's power supply stage capacitors. I haven't checked, but presumably there are two capacitors, one at the car '12V' input (which will probably be higher than 12V), and one after the regulator which will be a constant voltage regardless of car. The amount of energy stored in the first capacitor will be proportional to the car's voltage squared, and presumably the power dies when the voltage here drops below that needed to sustain the regulators.

Again - still only speculation. It does need a specific sequence of events, which should make it easy to disprove.