I am experiencing what I believe is the same problem with the PowerMate from time to time. However, I do experience it even when the USB hub is only powered from the Mac mini. I first thought the problem was caused by a wrong cable or connector, but now I believe the problem is something (no idea what exactly) in the PowerMate driver.
Could you check your log whether you can find something there? I can see "PowerMate device removed" message when the PowerMate stops responding and then "PowerMate device added" when I disconnect and connect it again. Strange thing is that even during the time PowerMate does not respond, it is visible in the Apple System Profiler.