GM 4pin HEI run problem..starts..but won't stay running

It is bound to be in the ignition power. How do you have the relay set up? Can you tell if it is working? Here is how just about all 12V Mopars, at least from "around" 63 or so up until lean burn season work:

You have ONE ignition "run" power in the engine bay, called "IGN1" It is hot ONLY IN RUN.........it goes COLD in "cranking" THIS IS PROBABLY the trouble

The second wire which IS hot during "start" is the coil bypass circuit. This is one usually brown wire known as IGN2. It goes from a separate dedicated contact on the ignition switch, to the coil + side of the ballast. THIS IS PROBABLY what is allowing the engine to fire

You need to determine where IGN1 and IGN2 come out of the bulkhead. Or, access the ignition switch and start there. Make certain that IGN1 is "hot" in the run postion. Check your relay, if it's powering the voltage regulator and ignition, you are probably triggering it from IGN1

See if the relay triggers, (should hear it) and see if it has power to the contacts, and then obviously, see when the key is on if power is going OUT
"Standard" relay diagram if you use the larger size:

best-wiring-diagram-for-a-5-pin-relay-simple-5-pin-relay-diagram-dsmtuners.jpg

30 should be full time power coming TO the relay contacts through a fuse or breaker. Make sure this is hot at all times. Typically, you might feed this off the large stud on the starter relay

87 is the controlled load. This should be what feeds power TO your ignition, voltage regulator, etc

85 is normally ground. Make certain it is so. This is also a good way to add a series unobtrusive switch, for theft protection

86 is the trigger voltage to energize the relay. this normally (in this case) would come from the origininal "IGN1" coming out of the bulkhead. Key in run---relay is energized