I had the same problem with my 88 560sel. Replaced the fuel pump relay and it is running fine.

Don't fool around with this problem. When the engine stalled, you lose power steering and brake. It can be very dangerous driving without these two functions under certain road conditions. This is my personal experience living around mountainous area of CT.

The stalling happened once awhile at beginning. I thought it had something to do with rainy weather. Then the frequency increased dramatically. Within a week, I ended up have it towed. It could not go far enough before it stalled again.