Truck died

Hi to everyone, I posted a problem I have with my 91 silverado 305sbc it just died going thru the parking lot. Turned key on and no noise from the old fuel pump and none from the injectors as I cranked it over. Sooo while thinking what I was going to do 75 miles from home and about 20 mins later I turned the key on and the pump started working and the truck started and I drove home no problem.
So now about a week later I went to the dump and it died as I was leaving, so I had AAA tow it home. Again after the tow home and 30 mins later turned key on and the pump started working and the truck started right up. I did all the checks and removed the fuel pump relay while the truck was runing and the truck kept on running, did all the rest of the fuel system checks and everything checked out. So why would the pump work after 20 or 30 mins of being turned off, any suggestions, thanks.