One thing that did cause this for me was having iStat Menus installed, with the Intel temperature sensor extension. The latter tries to get lots of hardware information for stuff the Mini 9 doesn't actually have but the software assumes it has (fans, temperature sensors) and under certain circumstances it locks up.
The solution in my case was to completely deinstall iStat Menus and its support directories in /Library and ~/Library.
Because I missed the functionality, I tried MenuMeters, which was rock solid stable. However, I found that although it worked, MenuMeters didn't give as much information (e.g. top CPU-hogging processes) so I have since reinstalled iStat menus *without* the Intel extensions. This means I can't sense temperatures or fan speeds, but as there is no fan and the temperature sensor didn't work anyway, that's actually no loss at all. It's only been 24 hours so far, but it seems stable. I've had one lockup, but I think that was due to something else.
If this is your problem, then it's pleasantly easy to solve. Otherwise.... good luck!