The player uses practically no power at all compared to your amplifier. If your voltage is getting pulled low the player will suffer, but the player itself couldn't possibly cause that much drain without blowing its fuse.

When the unit comes back up from one of these brown outs, does it show the battery icon in the top left corner? If so, that confirms that your voltage has dropped under about 8.5V and you need to consider checking your battery, alternator and wiring. Even old cars should be able to keep it up higher than that (I guess there's always viagra).

Rob