Check two other things:
* Lint in the charge port
* Battery failure on the case (even when it's rare, it happens).
Try to reset the case and AirPods and see if that helps: https://support.apple.com/en-us/HT209463; if not, the case battery is bad. In this situation hopefully, they are under warranty because the case cannot be easily serviced to replace the battery due to how it is sealed; it's basically disposable.