I have a problem in my Mini. My car have 41000 km (or 25500 mile), when I purchase the car had no problem.
After 500 km I made a general service (change oil, filters, etc). Since this moment, when started the engine (in the morning, when the engine is cold) I don't have problem with the pressure (My Mini have the sport chrono), immediately set on 1 BAR. But, in some case, when the engine is hot ( 90 Cº or 194 Fº) the pressure not give up until small accelerated, since this moment the pressure is always kept well, and never drops while the engine is turned on.
If the car was ok before the service the only thing I can think of is that you may have a bad oil filter
Some aftermarket (non bmw) oil filters can cause bad oil pressure and oil flow, if you have not used a original bmw mini filter I would say start there it is a known problem.
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