I had the same problems with my car... to the point that I didn't even want to use it anymore. It sat in my garage for two months before I came back to this forum and got a reply from MBDOC (thanks, again!). Anyway... here's my story.
Car started stalling intermittently. The red LED in the battery compartment (next to the diagnostic terminal) would light up. It could be reset by removing the battery terminal, but the problem persistently came back... sometimes after 10 minutes! So, the following things were done:
1) cleaned filter... suspected bad O2 sensor. No good.
2) Replaced O2 sensor. Still no good.
3) Brought car to reputable shop, wherein they began to tear into the engine. Car used to be my brother's, and he did ZERO maintenance on it. They replaced the distributor cap, rotor, spark plugs, wires, and then.... changed one of the fuel pumps (mine had two). Dude said, "Car's all good." I took the car out and as soon as I got on the freeway.... put-put-put.
91 Supercharged Miata
99 E320 Wagon