I'm pretty sure I know what was causing the ministick to stop working during a flight. Looks like the X52 profiler software is freezing/crashing whenever I load up a profile, with the added kicker of bluescreening my computer when I shut down or unplug my X52. The MFD also seems to freeze when this happens. Unfortunately, I haven't been able to find anything about this specific issue. I've got what I think are the most up to date versions of drivers and software for Win7 64-bit (6.0.4.1 and 9.9.9.9 respectively), so I'm pretty much at a loss as to what would be causing this.
In the mean time, I've re-mapped the HOTAS Slew control to the hat on the throttle, and that seems to be working out pretty well.