Lawn mower stalls then won't start

I have the same problem. Snapper riding mower. Runs for a few minutes, then sputters and stalls. It won’t start back up right away, but if I let it sit a while, it re-starts. The fuel filter was junked up, so I replaced that. Someone suggested the fuel cap vent may be clogged, but that’s not the problem. I’m thinking it may be the fuel intake from the gas tank, but I’m not sure whether that’s realistic.

Eureka! My guess was right. I took the seat off, then removed the gas tank. I emptied the old fuel and found that some debris was in the gas tank. (Last year one of my dear children cut the lawn with the gas cap off). I pulled the fuel siphon from the top of the tank and blew on the end closer to the engine. Voila! Out flew a 3mm diameter seed pod of some sort that was floating in the siphon tube. Obviously, what was happening was that when the engine started, the seed was slowly drawn through the tube until it got to the connector, which was too small a diameter to admit the pod. At that point, it formed a ball valve and the engine quit. If I waited a while, the pod slowly sunk down to the bottom of the tube. Kind of a weird problem. Probably won’t ever happen to anyone else, but that’s what my problem was.