Welcome to Mercedesshop.
You'll probably get alot of replies on this one.
What I believe will prove to be the problem is the overvoltage protection relay. It protects some of the control modules from voltage spikes.
It is located in the area behind the battery. There is a black plastic shield behind the battery, just push the top lip of it down and then remove it. the relay I am talking about is distinctive in that it has a clear plastic flip-open lid on top with a 10 amp fuse under the lid. In a case like this, I'd say the fuse is going to look fine. They had a few years back then that a solder joint in the relay would intermittently open circuit and the stalling at times was the result.
I would recommend replacing it. I could get the part number of the relay that was considered "bad", I know it was made by Siemens, and I believe the bulletin said that it was made in either Austria or Hungary. The new relay is redesigned, haven't had problems with the new ones at all. I believe the new part is from Belgium. "no one makes an overvoltage protection relay like a Belgian!".
Like I ay, you'll probably get alot of other folks verifying this problem, it's a well documented concern. The new part I believe is under $75, not too hard to install, you may end up removing the battery to do the job, but that's not that bad of a job.
You can check with this website for the part (partsshop or fastlane).