One item to check is the fusible link on the fueling system power wire. You'll notice 2 wires coming from the positive battery terminal...a really big one, and a smaller one. The smaller one is dedicated to the fuel pump/injectors & various injection-related sensors.
When the car cuts out, the first place to check is the positive terminal block on the firewall. There is the one that the huge wire goes to, and there's the one that the smaller wire goes to. They are electrically separate. Test for 12V on the smaller wire's block. If it isn't giving proper voltage, then the fusible link is the likely culprit. Sometimes the connections corrode & lead to all sorts of havoc. I was plagued with weird injection issues for years until I realized that I had made a bad repair on it. It is located about 24" from the battery, under some shrink tubing.
If it isn't that, then it could be a faulty relay. That is fairly uncommon though. The FP relay is under the plastic cover on the firewall, sitting with the main & oxygen sensor relays. I can't remember which one is the FP relay (the blue one, I think). I know the orange one is for the O2 sensor.