[adfields]

This sounds like a poor connection of the main power supply wire that runs from the starter solenoid across the core support to the under hood fuse and relay box. With it running start wiggling and pulling on that wire harness and see if it tries to die, pay extra attrition to the fusible link at the starter solenoid.

Next though is a poor ground in the PCM harness, try adding a ground to the PCM.