Check the fuel pressure - internal leak test.

I don't know about your specific car, but cars have a check valve or two in the fuel system to keep fuel from flowing back into the gas tank when the car is shut off.

Also many Mercedes have a fuel "accumulator" or "damper" which is a mini "pressurized fuel storage tank". Those hold a bit of pressurized fuel after the car is shut off (like a water well water storage tank).

Also those vent into the fuel return line and have a diaphragm inside them. If that diaphragm is leaking (internal leak), fuel will circulate right back into the gas tank and have trouble building up pressure.

And with the above problems, the fuel pressure will not be maintained after the car is shut off.