I had that symptom once, then It only started while vehicle engine was running, then not at all. I just changed the control board in it but I haven't run it long enough to see if it cuts out. So I can't say if that is that problem. Originally I thought heat related too. Maybe it still is. However if you look under the tech forum here another poster has the same problem and there is a reply that in their case the gas cap sealed too tight and was creating a vacuum to the point the fuel pump didn't have enough suction.
BTW I had already changed my fuel pump years ago. I just installed a generic pump mounted outside the unit on my vehicle's frame along with an inline filter. Now it is easy to check or change the pump or filter should I need to.