Sounds like something electrical is getting hot
and causing the shutdown. Relays to the fuel
pump, or perhaps the main relay could be overheating
The other thought I had was the ignitor, if so equiped
might get hot and stop sparking, or your ECU is getting
warmed up and a bad solder joint might stop making contact
Look into the spark first, them fuel, determin what is stopping
the engine, and go from there.
Report your findings here
Wild