[Ed Wright]

Your son's scan tool should tell him if it is in open or closed loop. Only way that would effect it is if in closed loop the O2 sensors (It has an O2 sensor for each bank) has output/signal voltage pegged every high, causing it to pull all the fuel it can to try to lean it down, or signal voltage stuck very low, causing the computer to pour the fuel to it to fatten it up where it belongs. Both sides do this is very unlikely. One side would make it run very rough, both side's O2 sensors doing the same like all of a sudden is not likely at all. A scan tool would tell you in a heart beat, if you know what to look for.

If he can't see anything on the scan tool, unplugging the O2 sensors, and it no longer shutting off, would tell you if the problem is in that area. It may be an issue of something electrical getting warm before it fails, not whether it's in open or closed loop.

Simply watching the scan tool would tell you easier. O2 milli volts should toggle above and below 450 mv, several times a second. Scan tools up date too slow for you to see it all, but the voltage is up and down all the time. Switching something like 60 times per second.
Takes a very fast digital 'scope to see it all. Staying up or down will prevent going into closed loop. Voltage staying above .450 indicates to the ECU that it's over rich, staying below .450 indicates lean to the ECU.

When it dies,check for spark, fuel pressure and injector pulse.

My experience with parts store reman ECUs is not good at all. I would not just throw a reman ECU at it. I learned to buy ECUs at the Ford dealer, GM dealer, etc.