Fuel ail pressure dropping a bit fast. Either the FPR or pump letting it drop. Just as a helper turns off the engine clamp the fuel return line and observe the gauge; then do the same but clamp the input rubber tube instead. One will show fast drop the other will hold pressure longer (5 minutes +). That will pinpoint which way you are loosing fuel pressure. At the risk of nagging do the injectors and all the previously mentioned battery areas!!
Good - Fast - Cheap: Pick any two.
E23 735i; E30 318i; E32 735iL; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i