If you'll search here a little, you'll find much information on this problem. It seems to be either a slight loss of fuel pressure after the engine is turned off. This decreased fuel pressure is most important on a hot engine when the cold start valve isn't a factor. The check-valves on fuel pumps, fuel pressure accumulator, fuel pressure regulator and fuel distributor and injectors are all known culprits. Either start swapping parts or do a fuel pressure test. Another thing that sometimes works is an adjustment of the plate in the throttle body (but this one is tricky). I'm no expert here, that's why I suggest searching the board. I did go through this with my old 87 300e. I stopped short of the fuel distributor and pressure regulator due to the costs. The other parts all offered incremental improvements in the problem , but it never went entirely away.

Good luck

__________________
Bob Johnston
03 E55
Comand/Nav/Bluetooth/Ipod added
Black/black
(Oh man, this car is sooooo fast.)