OK, so I now have a warning message saying: "Increased battery discharge! - Vehicle battery. Increased battery discharge while statonary. Electrical consumers may have been switched off. Reset date and time if necessary. In the event of recurrence, have the system checked by BMW Service."
How can I know this is the battery that is slowly dying? Could it be something else that discharges the battery? Or am I not driving long enough distances (as Nanniepoo suggests)? I don't drive much and it's often very short trips... I'm happy to change the battery, but I'm hesitant to take it to the BMW garage, since they are very expensive just to do a diagnostics...