I wrote this because most of the posting seem to be wrapped around 11. x so I wanted to update the issue to 12.1 which I have. It is relatively easy to fix as I found out that simply pulling and immediately replugging the TrackBall USB plug from the Mini sets things right without going through a reboot. It seems like the trackball gets cut out of the loop when the system has a moment to ramp up something in background, thus the unplug and replug set the Mini to checking who it has unplugged, which it then fixes. I have just installed this track ball a week or so back and have downloaded the s/w twice but the problem persist.
As for how long is "left alone"
Usually an hour or so, even over night (I most always use sleep mode rather than off mode to let the background work continue). Today I did notice it locked up once when it had only been left for perhaps 20 minutes while I attended to another matter not using the computer.
I'll see what I can do about disabling the computer sleep function, which might be ok for troubleshooting but seems like a throwaway as a fix. It would be easier to cut the power wire and insert a push button I think. I love writing software when I can stick with it but as they say "when you find yourself in hole, .... stop digging" which is me and s/w usually.