Why does my 86 vette drive 10 miles or so and then want to die?

When it does it I can shut the car off and start it and it will run fine for another ten miles or so. Now the service engine soon light comes on when it starts cutting out.

on those early C4's they had an issue of water getting into the air intake and seizing up the engine....also fuel injectors had common shorts in them, sometimes making it so the car cant be started....idk if this is THE issue, but check out this link, it can help in the future http://www.corvsport.com/Corvette/C4/1985-1991/1986/C4_1986_CommonIssues.html

BACK BEFORE ELECTRONIC IGNITION. THIS WOULD HAVE BEEN A SIGN TNE COIL WAS GOING OUT.

did your corvette drive near a DODGE VIPER?? this is common practice for corvettes when approached by formidable opponents. lol.....just kidding.....