Stalemate

This game really needs a stalemate resolving mechanic that kicks in after a few minutes of combat.
My fleet of 2x Missile and 1x AA cruisers are fighting a single enemy cruiser. At 4x speed. My AA Tiger has 2 armors, 2 shields, and the enemy can’t damage it at all. The enemy has a PD module, and my missiles can’t damage it at all. It’s been like this for 10 minutes now. The ships are just standing and shooting for the better part of an hour, and they’ve yet to lose a single hit point.
This is ridiculous. This is my second GSB game ever, am I supposed to just suck it up and retreat? Is this common?
Why isn’t there some kind of overheat/ablation mechanic that kicks in after 20 minutes of combat, that lowers shield and armor values by 10%, and by another 1% for every minute after it?

I thought that a given battle would be terminated after three consecutive minutes of neither side inflicting any damage upon the other. Unfortunately, another process is at work here and it’s preventing a clean resolution to the conflict.

I have seen more than a few odd combat resolutions - among the most memorable:

A) Fighters vs. Cruiser: fighters are consistently (though slowly) damaging cruiser, cruiser is doing nothing to fighters. Result: Cruiser wins due to the “no winning with just fighters” rule that has been mentioned.

B) Due to map conditions (weapon ranges reduced 90%), no weapons can fire. Ships on both sides wander around the map for ~25 minutes until I got bored and stopped it.

My point being that the stalemate conditions appear to follow some line of logic I haven’t figured out. But they do appear to be there, somewhere.

So, ideas…
At 12:00, reduce all shield and armor resistances by 10%, and by 1% every one minute later.
At 13:50, make all anti-fighter weapons 15% stronger. (for the odd case of AA cruiser vs AA cruiser never damaging one another)
At 15:00, issue a command to all ships on the map to attack towards the center of the map.
At 18:00, shield regeneration and hull repair is no longer possible.
Not saying that the game should automatically add all of these. I’m actually just interested in the first. But these are mostly ideas what can be implemented to stop the pain of stalemates. And to make the campaign less dire. (Oh nose, he invaded with one ship that has 75 armor and a single point defense! I must retreat! pulls back a force of five plasma cruisers and two tanks)