...even after the damage is repaired by an auton dealer. Removing it after it's repaired fixes it.
This is probably also why game records occasionally list damaged armor segments in final equipment. It's based on whether it was damaged when it was installed, rather than when the game ended.
Might be similar to the reactor glitch.
Fixed in 1.7 Beta 5.
The change made in 1.7B5 appears to be that the auton bay's armor repair function sets the armor's damaged property to nil if it restores it to full health. However, this doesn't really address the issue. (And not just because the auton bay's armor repair is almost completely useless.)
In general, the damaged property of installed armor items doesn't match whether they're currently at full hp. In order for it to do so, either the function(s) that check whether it has the damaged property would have to work differently for installed armor, or every event that can damage or repair armor would have to change its damaged property if it's restored to or reduced below full hp. This would have no gameplay significance for the player's ship, since the process of removing armor causes its damaged property to be set to true or nil depending on whether it was at full hp. However, it might reduce the amount of undamaged armor segments that can be looted from wrecks.
So the only effect of installing damaged armor is to change how its name appears in certain places while it's installed. This includes the auton bay - "Armor: damaged segment of _____ armor[ (n% damaged)]" - and the game statistics screen, under final equipment. Whether the armor has the damaged property depends on whether it was damaged when it was installed, not on anything that's happened since, except now for using the auton bay's repair feature. Since distinguishing between armor segments with and without the damaged property is not useful in these contexts, and is even misleading in the case of the auton bay, I suggest that (shpInstallArmor) set the armor's damaged property to nil (while still setting its hp to half if it was damaged).
...Although the fact that the armor repair function is almost completely useless does need to be addressed at some point.
Fixed in 1.8 Alpha 1, as you suggested: we clear the damaged flag when installing armor.