Frigates may have double the armor, but anti-armor units have double the speed. They can keep up with your fighters and bombers. Hold Z + X to see the attack ranges of units, and position the anti-armor units off to the side where they can fire on the enemy outside of its immediate attack range. And send your shorter-ranged craft (fighters, bombers) into the fray.
That will greatly decrease your anti-armor losses, as they won't be under fire quite as much.