Some gas tqnks vent through the gas cap. There must be a vent, or else the fuel pump will eventually create a vacuum in the tank, impeding good fuel flow. If you take the gas cap off, and it runs better, it's an indication that the gas cap vent may be clogged. Sometimes, just banging the cap around when you're removing and storing it will clear the vent, and it will work when you re-install it. But if it starts running bad again, invest a few bucks and get a new gas cap just to eliminate the cap as a possible cause of the problem.

A partially clogged fuel filter can also cause a similar problem. If you have both a bad cap and a partially clogged filter, you can get some weird indications.

Given the inexpensive cost of filters and caps, I'd change them both and monitor the engine operation for a while.