It's hard to give advice in such cases, especially with someones expensive equipment on the line. It's also very hard to debug such intermittent events. I personally wouldn't feel comfortable flying it "for real" until I identified the problem. While it could be an obscure bug in the firmware, that doesn't seem to be the likeliest possibility at this point. Until you're sure it's the AQ board itself that is the cause, replacing it might be an expensive waste of time. I guess I would do a couple of things if it were me...
1) check the AQ board and all the wiring for poor connections, especially at ground points. I'd check the board itself with a magnifier to make sure all the pins I soldered are really well connected, again especially at the ground plane (which absorbs a lot of heat when soldering).
2) Figure out what is is really going on with the parameters disappearing or whatever. What you're describing should never happen, nor should firmware get corrupted after installation (during, maybe, but not once it's loaded). If that is what is actually happening, then something is very wrong. First step would be to reproduce the issue at least somewhat consistently and work from there to narrow down the cause. BTW a bad ground can also cause comm issues and weird param read/write problems, though there's error checking in the mavlink protocol which should prevent bad data from being actually used.
Are you loading params via BT connection? Do the problems happen when using a wired connection exclusively? You're not flashing fw via BT, are you?
I think it's very unlikely to reproduce the problem just by running the AQ for a long time. You need to "exercise" it somehow, ideally by recreating the conditions which led to the crash. I'd start by recreating the simpler parts, like "flying" it around with your hands, vs. actual powered flight tests. But you may need to reproduce the whole scenario.
-Max