This is not a solution but I have a similar problem (although not lately) with my 2008 750Li with 228 K miles. I replaced battery (registered) and alternator. One mystery I haven't solved is why the CCAs at the battery (900ish) and at the engine bay terminal are so different (350ish). Voltage is a few tenths V. less too. Again, not a solution, but maybe something for you to check.