I'm still learning about this car, sooooo different ( high maintenance queen).. ave you done any maintenance for the fuel system? Have you tried any fuel additives/treatment? Such as Lucas fuel treatment, Redline S1 or the Techron all I read about are pretty good. Also, have you changed your fuel filter? It's on my maintenance "to do" checklist. Also, do a search for MAF sensor, try cleaning it, might help.
Some things to try. I'm sure other members might chime in.
'03 745Li (sold)
'03 Acura TL-S
'02 Infiniti QX4 (sold & new owner totaled it 4 hours later)