I recommend that you pursue pauldeere's idea to clean the fuel tank screen first.
I suspect that your fuel tank has a large amount of debris that floats around on the bottom of the tank. When you run the tractor this debris builds up on the tank screen and effectively plugs it up. After the engine stops running, all suction stops and the debris gradually falls off the screen. The longer the wait, the better the engine will run because more debris falls off of the screen. After you run it for a while, the debris builds up again, and it shuts down again.
On my tractor (Ford 3600) the screen is attached to the fuel tank shut off valve, and you can access it by pulling the shut off valve. Look into the tank, and make sure it's clean. If not flush it out with some fuel.