Did you try to see if a reset of the SMC may be able to help the Mini and its use of USB ports?
For some other items, a reset of NVRAM may be helpful; either way, these seldom hurt to try.
• Reset the System Management Controller (SMC) on your Mac - Apple Support
• How to Reset NVRAM on your Mac - Apple Support
The power management or 'system management controller 'has much to do with most everything
but some items may be acting up. -- Also some whose drivers may not be all they could be, may
conflict. In a few cases and where they could be deciphered (by an expert?) the Console utility
generates system logs that are extensive. All activities are recorded by time increments.
Troubleshooting the USB tree of items, and being able to swap out peripheral parts, may help
to find any weak or contributory, or conflicting products that may be USB linked.
In any event...
Good luck & happy computing! 🙂
• Late 2012 Mac Mini i7 2.3GHz quad, 16GB RAM, dual 1-TB HDD, OS X Mavericks 10.9.5 •