You may have a situation where the ring grooves in the piston are not deep enough for the rings you are using. This would show by the rings sticking up above the side of the piston when the piston is held on it's side. IF the rings stick above the side of the piston , they WILL bind as the piston grows with heat and stop the engine from running. As soon as they cool enough , the engine will " start right up" until the heat causes the ring to bind again. You would be surprised how many guys have had this happen. After listening to all of the well meaning ideas others have given I feel confident this s what's happening to you.
'66 GT350H-3 time cover car - Car Craft July'77,Modified Mustangs and Fords Feb2011 ( w/article), Mustang Monthly June 2014. Bracket raced by me for the last 44 years. Yes it is a real one.
'68.5 R code GT fastback
'67 Ranchero 408W -427 glass hood
'78 F350 "Oleynik" car hauler
Ford Experimental parts collector