Check the wire which feeds to your distributor. I had this happen once on a car I had built---damn thing would fire and try to start, then as soon as I let off on the ignition start position it would die.----I did a lot of head scratching, but finally figured out that the way I had it wired the distributor was getting current when the key was in start position, but as soon as I let the key back into "run" position the current wasn't flowing to the distributor. I had wired the car up wrong. Back in the 60's a bad coil resistor would do the same thing----distributor got full 12 volts when key was in start position, but as soon as the key was turned to the normal run position the coil resistor (which was supposed to supply 8 to 10 volts to the coil to extend coil life, but was bad and passing nothing) the engine would die.