Check for clogged fuel filter, or fuel pump electrical connections. Sounds like something is getting hot. You might want to Take it to BMW for diagnostic. I just dealt with a similar problem on a 1200. BMW said it was the TPS. Sounds from my limited knowledge that you might have a bad coil. Hope this helps.
How often need to change the fuel filter for a 2001 BMW 325i?"
It is in the fuel tank.
inside the fuel tank
The 2001 BMW M3 runs on premium unleaded (required).
The 2001 BMW X5 runs on premium unleaded (required).
The 2001 BMW M5 runs on premium unleaded (required).
how to you open gas tank door on a 2001 bmw 530i
The 2001 BMW 3-Series runs on premium unleaded (required).
The 2001 BMW 5-Series runs on premium unleaded (required).
The 2001 BMW 7-Series runs on premium unleaded (required).
How do you oopen the gas tank on a BMW 528i