I got 5 Mini's here - all FileMaker Servers, different generations (OSX and FMS). They run! I've had problems with the first couple of FMS13 versions (admin access) - but they run 7/24. The oldest is a G4 running FMS10..
I have also a Mini as desktop - for all day use. This machine used to crash often. I realized, that it never crashed when I was working and tried to figure that out... It was the screensaver! I had that to display landscape photographs of my own. Some of those photographs must be too big, corrupt, whatever. I disabeled the screensaver - about a year ago. No more problems..
I would search outside FMS (ok, could happen in combination, network, power, whatever). As long as the mini's are not overloaded, they are phantastic IMHO