If your inbound messages have stopped working, we recommend you first review the information in the following article: Why don't I get inbound messages from KakaoTalk users?
If the issue persists, you may have recently modified the KakaoTalk channel configuration for the corresponding Conversation API app. To review your KakaoTalk channel configuration:
The Sinch Developer Documentation site contains comprehensive documentation and tutorials that demonstrate how we support KakaoTalk using the Sinch Conversation API.