My father in laws 300E had a similar problem, but the lazy a... never really looked at it till I had to go and pick him up with a tow at 3:30 in the morning. It turned out to be 2 things, for some time the fuel pumps located under the vehicle or under right rear passenger had started giving a whining noise, had that replaced and it helped but the car still quit on him or was hard to start, so I had the fuel pump relay replaced and that took care of everything for good, the relay is behind the plastic cover behind the battery. I think I should mention that his car as well as mine, are Euro.
Hope this info helps out, good luck.