I am assuming the battery was ruled out as a problem already, but was more leading to a bad connection. This being said I have seen batteries with bad cells and/or bad internal connections that have problems based on the battery warming up during charging or the car will need a jump start once with a while, but once jump started the car can work fine for hours or days.

Simple battery testing can rule out this as a problem.

But bad BST cable, bad engine to body ground, bad/loose connection at the under hood jump start connection or even the starter.

Bad starter, brushes worn.

Even seen ignition switch and/or EWS antenna around ignition switch.

Keep in mind the shade tree battery lead tester is using the headlights and honking the horn, usually a bad battery will show up doing this test after a no start. But if this works out fine, there could still be other connection problems in the path to the starter.

Voltage drop testing may need to be performed because you really need some connections under load to find they are bad. Search YouTube and/or the Internet for Voltage Drop testing ideas and methods.

Also remember to access the Hidden OBC for monitor Voltage as well. Not sure if the E53 has as bad a system to warn the driver there is a Voltage/Charging problem, but the E70 really SUX about notifying the driver there is some sort of Voltage problem.

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2008 4.8i Black with Tabacco. Black Y-spoke wheels and shadowline trim.