Rod,
I had an old Ford 300 inline that did this. Come to find out it was a clogged fuel filter. The filter was the kind that screwed into the front of the carb. It was so clogged that fuel would barely trickle into the carb. If you let it sit for a minute or two, the residual fuel pressure would slowly fill the carb bowl back up. Then it would start back up and run for another 15-20 seconds. Once the fuel drained back out of the bowl it would quit again.
I drove myself crazy trying to figure it out. Once I discovered what it was, I wanted to slap myself for not thinking of it.
