We have had the same problems with the CDM1550ls+ in our combine. I think what happens is it turns on with the key (you hear the double beep) but the gps monitor is somehow backfeeding into the powerstrip and the radio doesn't turn off with the key (our radio is behind mounted on the box for the manual, so no one looks to see if it is off on the way out of the cab). Or that's what was happening with ours. Every year when I put the radio into the new combine i spend about an hour trying to chase it down. I gave up, there is a master battery cut off switch on the battery box in front of the right rear tire. Every evening, shut down and walk back there and flip the switch. Takes all of ten seconds, and haven't had a dead battery since.
Good Luck