A faulty fuel pump relay would make your car die as you have described.

Easy fix. On my car it's located next to the Overvoltage Protection Relay (it's a silver relay with a black or red top next to the control unit behind the battery - get it? ).

It's a black rectangular relay that has the word "kickdown" printed on the label on top of it.

Good luck.

Azhari
Babybenz 1991 190e 1.8