Engine Problems

[62ChevC10]

I have a 1962 Chevy C10 Shortbed completely stock. I am having some problems with the inline 6 motor that is in it. After not running for 20+ years I finally got it to start up. However, it will not idle for very long. I will turn the key (a few times) and the engine starts up and sounds great. Then after a few minutes of it idling, it just shuts off. I have changed the idle to high and low and have kept a really high idle by using the gas pedal, but it still turns off.
It also has a new fuel pump, rebuilt carburetor, new gas tank, new hard line, and new filter. Any ideas on whats wrong would be greatly appreciated. Or maybe it is time for a new v8 engine.