Tip: when you are losing carriers vs. carriers case.....
Carriers need to fall back and regroup. Period. No matter any situation.
Here's a thing; the problem is when your fighters and/or bombers got eliminated by his airforce, there is 0% your carriers ever produce fighters to contribute the battle.
Carriers make strikecrafts quite slowly, and this means as soon as new fighters are building, the enemy's fighters will kill them instantly.
In the end, your carriers would not be able to place a single squadron, making your carriers, all of them, completely useless.
It sounds quite too boring, but surprisingly too many players do not recoginize this issue.
Make sure fall back to near planet, wait for all the strikecrafts made and AM being refilled.