Why is -400 MSL the threshold? 0 would be the naive bug. I wonder if it's related to the geoid correction for altitude, which can be as much as -106 meters. That's close to -400 MSL. https://en.wikipedia.org/wiki/Geoid
Another thing to consider with modern avionics is this isn't a hand held Garmin or an iphone. There are two interesting military, and increasingly civilian, avionics features, GCAS ground collision avoidance system and TAWS terrain avoidance and warning system. GCAS theoretically engages the autopilot and pulls up if the plane is about to hit what it thinks is the ground. GCAS has already saved at least one F16 pilot's life, probably more by now. TAWS is about the same concept but rather than "don't hit the ground" its "don't hit the radio tower in front of you" which is somewhat more complicated to calculate both the danger and how to safely avoid it. Either GCAS or TAWS might have freaked out and "fail safe" design means you're better off shutting off or dumping into a reboot loop than letting something detected to be freaked out take over the plane. I specifically listed "or" because nothing fires off a fail safe quite like having GCAS report all is chill and calm while TCAS vehemently disagrees (or vice versa). I am a little unclear in avionics in general what happens when a GCAS and TCAS disagree. I guess TCAS only avoids obstacles by turning or climbing whereas GCAS only avoids obstacles by climbing (obviously?) so as long as they both implement that protocol they should never disagree. Unless there's a bug in only one of them below 400 feet.
Finally the verbal description of the problem indicates the nav gear failed after reboot but operated fine until reboot. My guess is the GPS firmware itself might have an "issue" in its acquisition firmware where obviously all positions below sea level are categorically unable to be accurate during acquisition mode so you can toss out any interim solution and keep acquiring if you find an altitude below -400 feet (see first paragraph). Or the GCAS or TAWS do the finite low pass input filter thing over multiple location data points where the last 60 seconds of flight data show a smooth descent to -1400 feet or whatever so thats perfectly fine because the boot up self test is not running while the system is booted, but on boot up during self test the input data filter having an output of -1400 is "obviously" a software bug so keep on rebooting until the input data filter has a reasonable value.
https://en.wikipedia.org/wiki/List_of_places_on_land_with_el...