[pat in Santa Cruz]

first thing, when it stops, remove the gas cap and listen carefully . Does it make a sucking sound as air rushes into the tank? that's a bad cap. Drive it with the cap loose. If its the cap, that will stop the problem, so replace it with a good one.

it does sound like fuel flow restriction, but could be electrical too. Does it spark when its dead? if not, check coil or condenser.

If it sparks, check fuel flow. Some causes of restriction:
poorly vented cap

junk in the tank clogging the outlet. Use a flashlight and look.

junk in the shut off valve.

junk in the sediment bowl

fuel line extends more than 1/8th inch beyond ferrule at either end of the engine compartment line

junk in the carburetor screen

junk in the float valve

junk in the main jet

junk in the channel below the main jet that periodically floats into the jet ..remove the drain plug, draining gas into a cup and check.

remove the fuel line at the carb, flow should be strong, not a dribble. Some guys say it should flow like a 14 year old, not a 60 year old. If its strong, look in the carburetor for problems. If its weak, isolate the problem by checking for flow out of the shut off valve. If its weak, the problem is in the tank or valve. If its strong, the problem is between the valve and carburetor.