The Delco-Remy starter/generators will get too hot to keep your hand on it.
When your engine dies, does it spit or sputter as it is dying, or does it stop as if the key is turned off?
Sometimes a failing ignition switch will cause what you are experiencing.
Is the fuel line getting so hot it's causing a vapor lock?
Are the points clean or is there any oil mist under the point cover? ....I once encountered a Wisconsin engine which got oil mist on the points after running awhile. ....The engine would die, but restart after 30-45 seconds, which was just enough time for the oil to drain off the points, restoring continuity thru the points.
Are the valve clearances set properly? .....When the engine cuts out, does it sound like it lost compression?
Lots of possibilities, but without further testing and more info, we're all just guessing.