As stated by many, a slow subtle change is what you would expect from burn-in or power. You would also need to turn the unit on and off. A momentary change, it sounds bright and then it sounds smooth or vice versa can happen once or can happen each time a unit hits temperature. This usually happens with tube units but in a SS device that is on all the time, it has to be a sudden change in what is being fed to the unit or the unit is defective.
Power generally doesn't have sudden changes. One exception might be if your air conditioner is going on or off or some other unit that requires huge power. This is often accompanied by the lights dimming for a second.
I would be biased toward some other problem if a Mac Mini wasn't involved. I have had so many customers have bizarre problems (DAC can't get IP Address, Cut outs, noise, skips in certain tracks, etc...) with Mac Mini's that I am prepared to believe they can and will cause any issue.
An easy test would be to set up your server on another computer of any sort and see if the problem goes away.