I can only guess
Since everything else has been changed, it has to be a fault in the power supply.
Is this a stock radio? IF not , it might be something as simple as someone tapped into a wrong power source and a safety feature is shutting off the power to the radio. There are a bunch of possibilities, and in the posts I read, many bad choices for a radio power tap.
IT sounds like a possible short, something is triggering a protection circuit, since it always triggers in the same way and resets repeatedly.
Could be worn insulation , loose wire, I suspect the brain doing the power cut might be in the computer, and if the fault is there, good luck.
I am not qualified to give this kind of advice, just trying to help , and not exceed my skill level , which is low.
THe bright side is that I have no idea if the safety breaker on your radio circuit is in the computer, and is malfunctioning, causing the problem. All I can do is guess , but it sounds like a protection circuit is being tripped , the most common reason would be a short ,look for signs of burns , anything that looks unusual.
It could also be power demands above what the circuit can provide, but that unusual, guys with big radios post other problems, not power feed.