This is a tough one. I had a similar issue with a non-BMW car. In my case, it was CMOS latch up in one of the electronic modules. The module was easy to identify because it would get hot. Wait until the car is back in the high current drain mode and look/feel for warm spots where the modules are. At your drain level (about four watts) that should be enough heat to detect unless it is in a module you can't get to or is spread out.
Your problem may or may not be CMOS latch up. If it is, some event (usually a voltage spike from a motor or solenoid) will cause the latch up condition. The condition will remain until you disconnect power or the battery goes too low. After that, it won't come back until another spike triggers it.
Alternately, you may have some module that is not always going to sleep for some reason or other.