I had a similar problem when the car just stopped running. I was getting spark and thought I was getting fuel but the pressure was not enough to open the injectors. The pump was running but the pressure was to low for the car to fire up. Like you, the car would start with some starter fluid but would die soon after. I tried messing with the mixture screw but it would not start. I finally got a fuel pressure gauge and it showed about 60psi(enough for EFI but not CIS). Replaced the external pump and runs great now.
Check the pressure in the fuel system. Just because both pumps are working does not mean it is working correctly. RM
