You can use the settings on the Settings > Inbox Settings > Inbox Organization page to automatically close a conversation when a contact stops responding. This allows you to better organize your inbox so that only active conversations are listed in the Open folder while closed conversations are moved to the Closed folder. By default, a conversation with no response is automatically closed after one day.

To change your Auto-Close Conversations settings, click the Auto close conversations dropdown menu, select an option from the list, and click Save.