The car is a '88 Trans Am with the V8 5.0l engine (engine code F).

I've been fixing it for some time now and finally has started to run rather nicely. There's some vibration and perhaps a tiny amount of rough idling sometimes when I stop on the traffic lights (and keep the transmission on D) but nothing special.

Lately there has been a new problem. Usually the car starts great. But about 20% of the times, it starts and immediately stops. There's no roughness to it, it doesn't even try to stay running, it just stops. Almost as if I've turned the key from start straight to off.

I've found no pattern to this. The engine can be warm or cold, it doesn't matter. Might do it after a long drive, might do it after standing for a few days.

It's not a big deal since if I give it a little gas for a few seconds, it usually stays running after that. But would still like to know possible causes and stuff I could check.

Any ideas?