I propose that if nobody on any allied ship has looked in the direction of a spotted ship in a certain amount of time, even if the spotted ship hasn't disappeared behind clouds or obstacles, and the spotted ship through its own action causes its angular position relative to the spotting ships to change enough since the last time anyone looked at it ("it's not where we expected it to be"), the spot will get lost. By "own action", I mean that if allied ships move considerably but the spotted ship is stationary, the spot won't get lost.
The intent is to increase the need for managing the situational awareness of a crew: if an enemy ship is behind you, but all engineers are looking at components and all gunners and the pilot are focusing solely on blasting the ship in front of them, then it seems reasonable that the approaching ship shouldn't have to take extraordinary measures to lose their spot. To make this work really well, the spot reticule would have to be simulated along the movement vector from the time it was last observed, so if you last saw a ship approaching you directly from behind, but nobody looks at it for a while, the indicators will still indicate it's facing you and presumably getting closer along the same movement vector; when you do finally look back towards it, if it's in the same direction as it had been (maybe within a 30 degree arc), the spot will be freshly updated without any action, but if it's not in that same direction when you look, the spot will be lost immediately. To display the staleness of a spot, all indicators could slowly gray out of existence.
In terms of time expiration, if it is feasible to involve line-of-sight calculations (you can't freshen a spot by looking in its direction when it's visually obstructed by your hull, even if it is following the predictable path), then it might be reasonable to expire a spot in ~30 seconds. Otherwise, if those calculations are not feasible, ~15-20 seconds seems fair.
As a side-proposal, it'd be useful for a flaming ship to be more easily spotted through clouds (similar to the flare effect).