Note that the fuel pump only runs when the engine is revolving, so if it dies for some other reason, you won't hear the fuel pump running.

OVP can cause it, though you'll have other symptoms like the ABS light lit when it goes down or no dash gauges.

Could be fuel pump relay (common).

Could also be ignition. Check cap & rotor, especially if not done by yourself or in recent history.

__________________
Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]