Lawn Tractor Keeps Stalling?

I have a Craftsman 18.5 twin that will start but only run for a minute or two then die. If I use the choke, it still quits running. If I smother the carb with my hand, it chokes it enough to run a little longer. I replaced the fuel filter and cleaned the carb. My thinking is that something gets hot and cuts the flow of fuel. Also, it's gravity fed and the vent on gas cap is clear.