Mac mini (Mid 2011) randomly reboots, but not while I'm using it

Very strange issue here. My Mid '11 Mac Mini (on OS X El Cap, 10.11.6) is randomly rebooting during the day and (mostly) at night when not in use. I will be up in the middle of the night getting some water and hear the Apple chime. Worth noting, I have never seen it reboot while I am using it.

I've searched for anything that says "kernel" in the Console program in OS X, but all I see are "PM kernel: Sandbox" items...are those related? Any help here much appreciated. Thank you!

[EDIT] After running the command syslog | grep -i "shutdown cause"from Terminal, I get 271 instances of the unexpected reboot over the past 5 days, all with cause of -128

Oct 28 11:02:59 localhost kernel[0] <Notice>: Previous shutdown cause: -128
Oct 28 11:37:54 localhost kernel[0] <Notice>: Previous shutdown cause: -128
Oct 28 12:07:55 localhost kernel[0] <Notice>: Previous shutdown cause: -128
Oct 28 12:35:52 localhost kernel[0] <Notice>: Previous shutdown cause: -128
Oct 28 13:56:05 localhost kernel[0] <Notice>: Previous shutdown cause: -128
Oct 28 15:52:22 localhost kernel[0] <Notice>: Previous shutdown cause: -128
Oct 28 16:03:45 localhost kernel[0] <Notice>: Previous shutdown cause: -128
Oct 28 16:26:52 localhost kernel[0] <Notice>: Previous shutdown cause: -128

This repeats many, many times with entries throughout each day. Click here to see the full log

Solution 1:

This ended up being a software issue. A clean install of the OS fixed the issue. I could not get the recovery partition to boot, so I had to use another Mac to create a bootable USB installer for macOS (downloaded from the App Store).

Worth noting, I was able to put all my apps and settings back into place via Migration Assistant, BUT only after booting into macOS (not on first boot during setup where it prompts for Migration Assistant - it failed there for some reason).