You may want to look at the plastic tube that goes from the PCV valve to the emissions valve.
This plastic tube can develop small pin holes or break and will cause this exact condition.
Must keep foot on gas to keep engine running.
I had my fuel pump go bad and the pressure test wouldn't show anything.
It was infact bad on the prime cycle.
i.e turn key, don't start engine, it was priming at 5 psi each key cycle.