My understanding is:
During crankshaft rotation, the CPS sends a signal to the EZL (ignition control module), which in turn (thru some additional electronics) makes the ignition system work.
So, faulty CPS = no ignition.
And flakey, temperature-sensitive CPS = flakey, temperature-sensitive ignition.

roughly you are correct

cliffmac,

What is your reasoning for thinking it is not the Crankshaft Position Sensor?

Another thing is, when it starts stumbling, if I press the accelerator and increase the RPM, it runs smoothly at the higher RPM. And I read somewhere that the AC voltage from the CPS increases, when RPM increases.

I want to be corrected if I'm on the wrong path here.

OK....sorry...anyway, I don't think it's the CPS. This, to me, seems more like a coolant temp sensor (CTS) issue...the CTS is a very big player in variable engine dynamic managment which of course Mercedes Benz employs. Let me think here.....

OK - here is the most basic reason... if the engine starts, it
is NOT the CPS...that's really it....the CPS will NOT affect the engine
operation once the engine is running...that's it..it's (CPS) out of the loop.
Once you shut the car down and let it cool off..and then can restart the motor.... that eliminates the CPS thing...dig? or not?