Battery discharge problem
 

So my E61 '04 has been acting strange lately.
Last week I didn't start for two mornings in a row (first cold nights this incoming winter, around -5C). I check the battery (changes it last winter, 90Ah AGM) and saw that it was discharging quickly. So I bought a new battery and coded it in with NCS Expert and registered it with INPA.
Still no luck.
At night when I park my car the charge is around 12.6V, and in the morning its around 10-11V.
Tried to remove the IBS wire ( @ 4:14), and removed fuses 34 (Radio & Nav) and 38 (CD-Changer).
The discharge over night dropped a bit, but is still to high. (12.6V->11.8V).
INPA showed no errors concerning any electronics.

Anyone got an idea where to start to hunt down the problem?

Quick update:
I have done some checks with a multimeter along the night & day.
4.11 @ 22:30: 12.45V
5.11 @ 05:00 12.52V (2h charging at 4A)
5.11 @ 07:00 12.2V (4h charging at 4A)

How can it be that the charge rate is falling all of a sudden? Between 05:00 and 07:00 I only unlocked the car to access the trunk. Didn't start it or anything.

And for some reason my diesel heater (Webasto?) wont start as well. The remote shows the green light and the car interior lights light up but nothing happends.

Update 2:
The hidden menu says 12.4-12.6V (IBS connected), multimeter says 12.1V measured from the battery.