Slightly OT: e36 OBC 'resets' when key out
In a nutshell, put key in, turn to ACC, set clock and other fun things... take out key. Next time put key in and go to ACC, need to input time and things again.
So... where to start checking? Yes, there is a battery in the car.
Sounds like you have no keep alive power to the OBC, or the OBC itself is bad. check all the fuses.