If your AirPods Charging Case is not charging, try this before going to the Apple Store.
AirPods Case Not Charging Fix
There may be some debris inside the port of the charging case preventing it from charging. Try blowing into the lightning port of the charging case to remove any dust.
If this does not work, try using a different lightning cable (preferably an official Apple cable). You can try unplugging and plugging the cable in a few times to see if it will begin charging again.
If all of this fails, you will need to contact Apple or go to the Apple Store to get it fixed.