GB tractor shuts down after 15-20 minutes

My Great Bend tractor always starts easily (after a period of non use), but after about 20 minutes, it will shut down. Once that happens, i can't get the engine to run again for about 5-6 minutes. Once it is firing and running again, the engine speed doesn't respond in accordance with the throttle. By that i mean, i can put the throttle all the way up and the engine will not accelerate. i tend to have to keep it completely down or the engine will shut off. after about 5-6 minutes of that, it will begin to respond a bit more then eventually be fine.
after another 20 minutes, the process repeats.

Does anyone have any idea what is going on?