Can a damaged ceramic case be repaired?

Ceramic doesn't really repair like metal does. Chips and cracks can sometimes be filled with epoxy for appearance, but it won't restore structural integrity. If it's a hairline crack, it may propagate.

I've heard some watchmakers can polish out very shallow chips on ceramic, but deep ones are permanent. The crack near the lug is more concerning because that's a stress point.

Most watchmakers will recommend replacement cuz any repair is cosmetic at best and could fail. Ceramic is brittle, so a crack means the case has lost some integrity. If it's a daily wearer, I'd be cautious.

Depending on the brand, a replacement case might be available but expensive. Have you checked with the manufacturer? Some offer case replacement services, though it's often not cheap tbh.

I had a similar issue with a ceramic bezel insert. I ended up replacing the whole case because the repair quote was nearly as much as a new case. Not sure if that helps, but it's a data point.

Also, if the crack is near the lug, water resistance is likely compromised. Even if you repair it cosmetically, you'd have to be careful about moisture. Might be worth getting it pressure tested after any repair, though it may never be the same.

That sounds reasonable. Just be aware that if the crack grows, the case could fail completely. Maybe avoid dropping it again.