Sorry for another double post. After some more experimentation, I've found that strange behavior appears when the player uses an escape type ship to escape from a dying ship. The missions continue, but the outfit is removed (even when both "stays" flags/boxes are checked).

Checking "Fails if player is disabled or destroyed" does not work as a fix.

Try doing Axxx on acquire of the escape ship.

I'll give that a go. I think that will require doing the same for all ships, but that shouldn't be a big deal. Currently, I have the outfit move across ship changes for that very reason: the mission continues otherwise. If Axxx works, then I'll just apply that to all ships and make the outfit non-moving.

I'd like to point out that the "Fails if player is disabled or destroyed" flag does indeed work; the mistake was mine in having a copy of the mission in the files and the plugins at the same time, the plugin mission overwriting the Nova Files mission.