I've been working on this Miata. 2001 year model. I was getting power to the fuel pump but it would not start. I replaced the fuel pump. It now starts every time. It will start and then die. I can feather the fuel pedal and it will run until I stop pumping on it,and only if I pump it. I've replaced the mass air flow sensor with no change. There are no check engine lights. Engine starts for 2-3 seconds and dies. I'm going crazy, please help.

 

Have you done a code check?