I have read a few similar reports.

Without having the software to interrogate the car to look at BMW-specific module stats on charging, etc, we re stuck with rudimentary tools.

People like to get 'rifle shot' diagnoses, but sometimes you just cannot. They want the mechanic or store to 'test my battery' or 'test my alternator' to be certain they have the right cause.... the active charging system BMW uses can 'fool' this diagnostic approach.... Batteries go bad. After 4-8 years, depending on use, temp and other factors, it may be easier to just replace the battery to rule that out.

Here is the problem- the symptom you describe (battery crashing due to chronically low charge) can be due to lack of charge caused by bad alternator; lack of charge due to short trips and depleted battery; lack of charge due to bad battery.

At least thats my view.