I had the same on my car today, the wife comes home and parks the car in the driveway and the car shuts off by it self. Next time it's to be used it didn't start up, but cranked well. Seemed electrical to me, i read the threads and got to the indication of the fuel pump relay. No power on the fuel pump when cranking the car, I jumped 30 and 97, ( 7 and 8, reading the socket ), it fired right up. ( that's for mine 380SEL 1982 )

I belive it's about $135 here on fastline, well since I had to wait why not pull it out and look inside maybe solder joints, like happens on the idle box. Sure enough one of them looked cracked, took 5 min to solder and the car was running fine as before. I don't expect it to hold another 20+ years but maybe a couple.