When a target is scanned, revealing HP, Firepower, weaknesses, etc that information should be retained if the target flies out of scan range.

[Commander Corgi]

Scanning (getting close enough) to a target reveals important information.  However, this information is not retained if the target flies out of this range.

Omicron seems to remain, but hull and shield HP numbers do not.  Knowing a target's HP is important, and the player has already scanned that target. there's no reason for the targeting computer to "forget" this information.

Enemy ships with high firepower and low HP are priority targets, and retaining this information for ships that have already been scanned will allow the player to make more informed decisions in combat.

[TimingGauge]

 To play devils advocate, I would argue the thought behind this is that depending on the ships stats the values of HP and Shields are transient enough to warrant needing a rescan, whereas omicron rating/speed/distance are much more quantifiable.

At least, that would be the first reason I can think of that would require a targeting system to "forget" the info. It would be nice, but I feel like making it stay visible would go against what the dev's intended combat to be like. They had to code the distance/time/conditions for the information to be hidden or displayed and they chose it, I'm not sure if they would alter that. I hope you find a way to make the game more to your preference, have you checked the Workshop for a mod that might prove to be a fix?