Agreed,
Has anyone thought of checking the temperatures of the CPU and GPU with a temperature monitoring program?
Does the PC shut down when in safe mode?
Does the PC shut down when you have only 1 stick of RAM, each stick?
Have you ever thought of breadboarding your PC? This is the process of taking all parts out of the case and setting them up on your kitchen table. The you attempt to boot up the PC with the bare minimum of hardware.
Breadboarding rules out short circuits which will cause the PC shut off.
Bad RAM has been known to crash a PC.
You could have a bad motherboard for all you know.
Are all the motherboard mounts in the correct places? If you have an unused mount in the wrong location that's touching the back of your motherboard, it can cause a short.
Have you taken a look at Windows Error Reports on your PC?
Finding the answer is a process of elimination. Sometimes there are silly little things that can cause a PC to crash. Outside contractors like the Geek Squad or Fry's Electronics will only test a PC to see if it powers on but they will do nothing to see if it's running 20 minutes later. They don't know all the tips and tricks like how to check for a short or to breadboard. In a lot of cases they're just geared to sell more hardware to you.
Shipping an entire PC off somewhere is very expensive. By the time you paid for the shipping there and back, plus the repairs, you could have bought yourself a new motherboard and CPU.
You can't blame AMD here. If the motherboard is faulty then it's the manufacturers fault, not AMD. AMD systems are just as reliable as Intel's. There isn't as much truth to this getting more bang for your buck with AMD as people think there is. AMD just excels at certain pricepoints, or their processors are good with certain applications. When you spend $300 or $150 on a CPU, you are getting what you pay for.
It would also be helpful for you to list the specs of your hardware. You can also find useful answers at places like Tom's Hardware or maybe pcpartpicker. Tom's is more geared towards hardware repair. It would be helpful for you to find others who have faced the same situation and found the fix.
In the past I had a system that would shut off after 10 minutes to 30 minutes of use. I swapped all hardware and even tested with a different CPU. The motherboard at fault here. Once I replaced the motherboard they system was fine.