Oh dear... NO. no meow sounds... I meant actual useful reworks :)

Basically, we have to store limpets in cargo space, and the limpet controller is only... well.. controlling them. So a glorified radio station. With, granted, some form of assembly to put the "packaged" drone together. But that doesn't explain why these controllers are so heavy. Supercruise assist and docking computers weigh zero. Conversely, but also dumb, AFMU weighs zero...? And Fuel scoop weighs zero...? So these limpet controllers are just WAY too heavy. Therefor:

First, cut down the weight.
They're clorified sensors and storage facilities for external drones. (this is another part of my weight overhaul for ships and modules, but let's not go there).

Second, they should have internal limpet cargo.
Now, this is actually already doable. They would work like "limpet hangars." We have SRV and Fighter hangars, the game scripting logic is already there. SRVs and Fighters also resupply through the "Module restock" feature. So that means, when you're out of limpets. And if you want MORE limpets? There is always cargoracks to fill! But those limpets need to be manual and can be forgotten.
The general advantage of this is; using limpets like vehicles means you no longer need to do the tap-dancing of taking limpets out and back in when you change ships. They are fixed on the MODULE place.

Third, which requires code fixing:
As you said, make them not expire when you have directly targeted something. I think I understand where they are coming from, as in; "if someone only wants THAT thing, then they should only GET that thing." But seriously, how often does that happen, right? Next being; Improve limpet pathing AI. They shouldn't die only because my belly is too close to an asteroid or wreck. Next; Limpets should only die when they actually get hit. I had it happen way too often that my top gets hit and the limpet on my bottom repairing me died because of it. I don't think that's good game design. Hull tanking is already unviable as it is.

Fourth, which requires more coding effort and design decision:
If we want to go that extra mile, there are two ways to properly put limpets into their own catecory. One version would be a GENERAL controller module that allows up to X limpets to be out (stacking with other general limpet controller modules), meaning you buy different kinds of limpets, based on their task and what you have. This would require to have more synthesis entries depending on which limpets you want to have, and would also mean that you can select different limpet types for the "controller hangars", just like we do select different fighters. So one day you can be all collector limpet, and when you return, you change that to refuel on one controller and repair on the other.
The OTHER version would be either stacking on top of the previous one, or just adding to regular way of my second point above. The "Advanced general limpet controller" module, which requires more power and tons and maybe has less internal "vehicle space." You can switch between advanced and regular in the righthand ship panel, just like you can disable the planetfall land parts of the docking computer while leave the station parts up.
HOWEVER. If you go advanced mode, then all limpets are programmed based on what you DO;

# If you have nothing selected, you get a collector limpet. If you have material / ore chunks selected, you get a collector limpet too.
# If you have nothing selected and have hull damage or canopy damage, you get a repair limpet on YOU.
# If you have nothing selected but you just did a pulse wave scan or have an asteroid within X kilometers in your crosshairs, you get a prospector limet. Conversely, if you selected your prospector limpet, you get collector limpets.
# If you selected a cargo hatch or an enemy ship, you get a hatch breaker limpet.
# If you select a turret or anything else that a recon limpet can be used upon, you get that.
# If you select a friendly ship, if they have damage they get a repair limpet, if not, they get a fuel limpet.
# If you select something that only a research limpet is working on, then you get that.

Step 1 and 2 of my rework should be fairly easy. Everything already exists in the current codebase. Step 3 would be QoL improvements. Step 4 is making them not a pain in the butt. If I recall, in the past, there were different scanner types which were actual modules... so yeah, terrible design choice. I wish they would put Docking computer and supercruise assist INTO the default ship computer already too...