Runs then dies

Another thing to check is the short jumper, at the back, from the sender to the hard line. It doesn't usually leak because it is above the Liquid line.
Here's my take on what happens;
if your pump is sucking air there, it will pump it up stream into the carb. Thus the pump loses it's prime. After the car stalls, the fuel in the supply line comes together in the lowest part of the line, and with a lil cranking, the pump gets it's prime back. But now the pump is working overtime to fill the line ahead of it, and so once the carb is filled, you get another block of time out of it. Then with the pump idling again, it starts to pull air again. Or maybe I should say, the pump begins to pull more air as a percentage of the total of what it's pulling If she starts to get 30/40 or 50 percent air, well, you get the picture. Sooner or later the pump will starve.