Markus, I appreciate your support. I am a bit intrigued too on the insistence of Dave and Kem that it must be the internal power supply. It could very well be, but a random issue in a machine that is notoriously difficult to open looks like a challenge to any repairman. Translated in dollars, looks like a small fortune and a long intervention. It is like a doctor saying without any examination “you’re a little fatigue, let’s do open heart surgery”.
Debugging hardware should proceed just the same way as software : start with the easiest and work your way inward.
If I remember right, Dave changed outlet, so chances are it is not the wall connector.
What is the state of the power coming in ? From previous conversation, that hypothesis was never verified in any way, besides the very dubious fact that laptops and the Pro run fine. That is far from being scientific. I suggested using a simple controller ($5.00) to verify voltage when a shutdown occurs. It would not show micro power interruptions or transient spikes, but that would be a start. If it shows voltage below 100 volts, then the culprit is found.
If voltage is alright then it could be short power interruption, as occurs when an electric engine starts, typically a fridge or some other appliance like an electric mower, a blower, a drill, whatever. The same thing also creates a spike. Ideal combination.
Now what are the reasonable options ? Trying the UPS costs around $100 for a well sized one. Then all is required is to wait for another shutdown that may never come.
If the shutdown still occurs, then there is certainty it is an internal power issue, and with that in hand, means taking the machine once again to Apple, plead the case with persuasion, and hope they will corner the bug. Chances are for a 2012 machine AppleCare has run out, so I would be extremely surprised if the bill runs under $200. As a matter of fact, since shutdowns manifest at random and weeks apart, Apple will most probably simply replace the power supply and not think further. If it is something like what Frederick suggests, then might as well buy another Mac. A motherboard is no peanut.
Now, this looks like the proverbial joke about engineers leaning under the hood of the stalled car. http://funnydot.com/jokes/Three-Engineers-In-A-Car.html
It is not my machine, and I have dealt with enough proponents of alternative medicine to know better than contradict religious beliefs. Personally, I do not use a crystal ball or a pendulum to debug things. Just hard facts and logic.