Doesn't the remote monitor for the keyless controller eat up some amperage while in the "wait" mode?

Same approach, no one has suggested the alternator, either its not getting enough run time ti fully charge the battery or isn;t charging correctly when it is run or the battery itself has a defective cell.

What you need to do is run a set of jumpers off the alt to your meter and measure output and run a set to the battery and see if what is coming out of the alt is getting to the battery.

Example: I had a Volvo that had a system that the trigger voltage for the charging system was passed thru the dash idiot light and when the bukb died so did the charging circuit. Possibility here?

I also had a client that found the existing telephone amp in the trunk was wired to power antenna circuit for power (belore the relay) and merely disconnecting the handset controller wiring from the fuse box did not totally kill the system or its electric draw. Ditto?

Sounds like you need a session with a good MB tech or a good 12V Tech.