Had same symptom 2002 4.4i. even bought a new battery from BMW. Many jump starts and trickle charges. Turned out to be the FSR. The fan that ran down the battery is almost silent and it only ran after shutting off the car every once or twice a week. one night after car sitting 30 minutes I could hear a very slight sound i thought was under the hood. Took 10 minutes to swap out. You can reach up and remove it via feel. I was an idiot and convinced myself it wasn't the FSR. it was.
Good luck.
Kevin

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2013 X5 E70 3.5d Black Sapphire