This sounds like an alternator problem. On an MB I had, the alternator worked intermittently but when it failed the whole car shut down and I literally coasted dead into an open service bay at a garage in a small town. Another MB had an alternator with a bad diode. It charged and checked out fine but then suddenly it would suck all the power from the car, killing it in the same way. If its an original alternator it may be time to replace it anyway so it won't be wasted money if something else is wrong.

 

It does seem like the alternator, good luck.