Ok so i recently bought a 81 z28 the car will start and run for a little bit then just shuts off almost like u shut the key off. I have been able to crank it after it dies and check for spark and im gettin nothin but after it sits for ten fifteen minutes it will start back up and run its only stayin runnin for 5 to 25 seconds i have replaced the coil the dist cap and rotor what could be my issue also it never loses power to the coil so i know its not a bad ignition switch

 

might try an ignition modual.

 

I'd start looking for a short. Maybe the vibration of the motor is causing one of your wires (with thinned out insulation) touch something metal. Just a thought.

 

Both the above thoughts i would try out, by any chance do you prime the carb before starting it every time? could be your fuel pump if thats the case?