Rob, I also had a 2003 BMW 530i with around 200k on it do the exact same thing. My step-daughter was the one driving the car (do to my procrastination fixing her Jetta), and lived an hour and a half away. When it would die on her, she'd have it towed to me. Of course, by the time AAA towed it to me, the car would startup and run normal. This went on for about a year, with maybe 4 breakdowns over that time. I finally had her leave the car for a week and I drove it. It acted up on me finally on a hot day in traffic, exhibiting classic running out of fuel type symptoms, also wouldn't restart. I had a stranger at the gas station I pushed it to crank it while I smacked the top of the pump cover with the lugwrench. It started and I booked it home, put my fuel pressure gauge on it and all was normal. I work at an Indie Euro shop, so I ordered a Valeo pump assembly for around $150 as an educated guess. It ran another year with no more breakdowns before getting T-boned by a guy running a Red light. Put a fuel pump on it.
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