Had a starter go out exactly how you describe on my E38 and have dealt with intermittent issues like this on an E39. The E39 starter would test just fine at Autozone, but eventually I did replace it and all has been fine since.

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'01 740i Sport MKIV, Quad Brake Lights, Bi-Xenon retrofit, HID Fogs Dinan 7 Struts, Springs, camber plates, Intake, MAF, CAI, Throttle Body, NBT Retrofit, Strong Strut


'99 318ti Titanium Silver; '97 318ti Boston Green; '13 X5 3.5i Saphire Black Metallic
'84 633csi Black (sold); '88 325iC Black (sold); '97 740iL Black(sold); '01 740iS Black (sold);'97 318ti White (sold); '08 X5 4.8i Titanium Silver (sold); '96 318ti Alaska Blue (sold)