I hope that the controller is your issue since you bought one but...
At this point you verified that both power feeds(RD/WT and DB) are still present at the ASD Relay when power output stops which leads to one of 2 problems...
1)You are losing the ASD Relay ground control which is the DB/YL wire and computer controlled.
2)You are losing the crank signal to the controller.
If you had a scanner you could easily tell(less than 1 minute) if the crank signal is the issue.
Go to Data Stream, look at RPM and crank the engine, if the RPM reading drops to 0 the controller is not seeing a crank signal.
Before condemning a controller you need to check 2 things.
1)All controller power feeds and grounds are present.
2)There are no "pushed out/spread/broken internally/corroded" terminals in the controller connector related to the affected circuits.