Check the charging voltage at the battery and alternator amperage output first, unless it's about time to change out the alternator anyway, but even then it's nice to know exactly what's going on. I think the rebuilt alternators are a bit of a crap shoot for quality. Taking a real life load out of the battery or alternator is the best way to test, there are some good threads on that and one of or members did a good summary. Also some good threads on checking for parasitic draw.
Checking all the grounds, the underhood battery terminal, alternator and starter connections always good idea and often missed. BST connection can be a problem but not so common.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)