I too think it could be a bad gas cap vent, VAPOR LOC, will do this as things warm up
so will ALL fuel flow issue's, HOW old is the fuel itself too??
simple problem shooting steps here
start with drain old fuel, inspect peacock, clean if needed, (also maybe screen in tank is plugged up??)
pull or better yet, replace fuel lines from tank to carb, there cheap and easy to do and rule out one maybe being clogged up?
once this is done, replace fuel with GOOD fresh fuel and see
if still there check cap for venting, when it dies, OPEN the cap and listen for air rushing out/in!
if that doesn't fix it, replace plug
if that doesn't solve it
come back and let us know and more idea's will sure to come! LOL