Runs then dies

Rinsed and blew air thru fuel cap vent. I will have to admit that I haven’t thought to try it with the cap off or loose.
Ran it twice more today. Although the first run the fuel filter remained full the second and third time when it died it was half and near empty respectively. I am starting to think of adding an electric pump , but am probably just taking a poor mechanics attitude of throwing parts until something sticks.
Yote
Sounds like a failing fuel pump, or a venting issue. As mentioned above, remove the gas cap and see if that changes anything. If it does not, I would replace the pump. By the way, the rubber hose that connects your metal fuel line to the pump inlet: if you squeeze the rubber, is it firm or very soft? If soft, I would replace that piece for sure and re-test.