From what we had in our old W124 230E, the same problem was encountered. The service technician said something about the fuel supply being ok when its cold, and then when the engine warms up - the fuel gets evaporated before its able to the combusted.
They changed the fuel pump and relay, and it worked well. I was sure they did replace something too, but I can't remember as it was yonks ago.
Maybe Benzmac may be able to recall something?
126 tailed by a 203, 129 leading the pack.