There are too many variables to diagnose it very well in this way, but here's a few thoughts:
Yes the engine is fuel injected. What the engine essentially needs to keep running are fuel, ignition and compression, I think compression can be eliminated as a possibility, so we can assume you are loosing either spark or fuel. It could be a complex "fuel injection" issue, or as mburman pointed out, as simple as improper octane or just plain poor quality gas, a fuel filter that hasn't been replaced ever, or worn out spark plugs or a bad ignition circuit (coil, controller, cap, rotor, etc).
I have seen several of these that act this way when the fuel pump or fuel pump relay go bad, they can act up ntermittently like this, and seem to happen alot of the time when coming to a stop.
One other possibilty I've seen is a bad idle control valve or valve control unit, this is more closely related to the fuel injection system, usually if it goes bad it causes an erratic, fluctuating idle, not a stall, but I have seen a few that would stall also.
If you want, you could let us know what the service history is on the car, for example the info mburman requested concerning when the car last had: air filter, fuel filter, sparkplugs, etc, but ultimately I think it'll take a date with a good MB tech, not a few questions at an internet site to solve the problem.....