I would begin by checking battery voltage and doing a load test. My experience with the E53 was that you only get 3-4 starts on the engine once the battery reaches failure point. There's very little "cushion" time before a replacement is necessary once the battery starts to go.

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2016 F15 x35i
2014 F32 428i


2004 E46 325i sold at 123,600 miles
2002 E53 3.0 sold at 388,801 miles
2001 E46 325i sold at 66,000 miles


1970 Firebird Under restoration