Yeah, the airgame is rough. That's why I suggested Cinematic mode, because it affects interceptors too.
You generally want to call an interceptor back as soon as it takes any damage because of repair times, which means unless you're save scumming, it can be a total crapshoot whether you actually get the enemy craft shot down. If you miss too many interceptions in the first couple months, the rest of the campaign will get a lot harder because of your slow start.
The difficulty of the airgame is why the beam laser rush is generally considered the best way to open a campaign. Improves both your ground game and your airgame, and laser cannons will carry you through the air all the way to tier 5 weapons, since Tier 4 weapons (pulse lasers) includes a foundry project that increases the damage of your laser cannons, effectively upgrading them all to tier 4.