My two most used Mac desktop computers (also portables when I've set up a desk space to leave them turned on)
are left on and allowed to sleep, and occasionally I restart them in Safe mode and repair permissions or boot from
a utility (OS X Recovery on newest, OS X install DVD on older) to check and test some aspect; or not usually after
a few months of being allowed to sleep when they will, according to settings of my choice, it's good to restart them.
The longest my Macs (for the most part, going back 10 years) have been left on, yet allowed to sleep; with displays
set to sleep sooner to save from excess wear or heat, has been eight months, on. With older OS X versions in old
hardware their status would be easily checked to see if the memory was being held in cache beyond reason, and so
a restart after several months would be an idea. I'd sometimes log out of one user account and into a second one
and that sometimes would allow me to not bother restarting, and test the system. And clones, for testing are good.
A backup of what you have in your computer now, for a reference copy (a clone?) that could be used to run the Mac
from outside, if testing did not change the issue; since a problem like you state may have hardware basis, is an idea.
You could backup the computer and then go into there and erase the hard drive; with these newer OS X versions
and their dependency for online downloads to restore the system, and special partitions in the hard drive that a utility
would likely destroy, the ability to use Internet Recovery to get the system from scratch (and from the purchased list
of OS X upgrades and previous included software bits) can be prone to issues. But that could be done as a test, if
you happen to have more than one computer to use one while the other is in limbo. I've found extra macs helpful.
And backup power supplies, those automatically switching ones where high/low grid power is filtered; has a battery.
Since most parts can be removed from the Mini (level of difficulty depends on if you expect it to work again later)
and replaced, troubleshooting the source of the problem is the important detail. Some software may not like to
play along with the hardware. There may be some 'startup items' or things that load first that are bad software so
they may be suspect in a bizarre voodoo clinic operation where you have to sacrifice some KFC after re-warming
or maybe a vegan soy chilli dog in the microwave. Along with a warm beverage; my fav is instant crystals coffee.
And some time to consider, to search for alternatives to just going crazy... Or if already there, going 'sane.'
Did you see what kind of bits an etrecheck report shows? I've ran a few and there was nothing untoward implied
but I don't expect to see any; for the most part my Macs just work. And I am aware of their hardware limits. Maybe
a full diagnostic testing interval should be done; that'd be a retail paid visit where you leave the Mac, for a few days.
Maybe someone else will look into this and laughing know the answer was a nearby ant farm whose stragglers
only were looking for shelter and warmth when they found a vacancy in your Mini hotel?
Apparently I haven't an answer except to create more than one type of backup (plus time machine) on more than one
external drive device, and see if an all-new installation from scratch exhibits similar issues. An external drive with a
basic installation that can be used to start and run the computer may be helpful. Also different user accounts can be
good to use where software may be a cause of odd issues, if those accounts haven't been exposed to the same odd
bits that may clash to create problems. Hardware based possibilities need to be isolated from software for discovery.
Good luck in this matter! 🙂