Poss. 'main relay'. To check an easy way, in a quiet area turn the key to the 'run' position ,(check engine light on)and watch the light , at the same time listen for a 'click' at the same time as the light goes out. May want to try that two or three times to get used to the sound. Then next time , after it stalls and won't re-start , do the same thing. IF you do not hear the 'click' when the light turns off , replace the main relay - it's bad. It's located under the drivers dash. Easiest and best is to have the replacement in your hand , to match -up what your looking for , if you're not familiar with it. May be awkward to get to.Easy , cheap test (free) before you spend money on a fuel pump you may or may not need.
Test the fuel pump circuit while it operating to see if the circuit closes when it dies, if the circuit is good and the pump quits anyway, change the pump. If not the problem find out what is causing it , distributer ?
That makes perfect sense and would be the reason for thinking it to be a fuel pump failure. That is a good test and explanation look at the last post and try to understand what he is asking you to do. Any questions just ask.