Intercom connections can break for different reasons. For example, if the connected app user changes their Intercom account password, they manually revoke the authorization token associated with the connection, or they are removed from the connected Intercom workspace. All of the previous actions will render the app's connection to Intercom unusable, and it needs to be reconnected to ensure the app is working as expected. This page explains how to reconnect a broken connection.
From the Jira home screen, click Projects (1) in the main navigation menu and select the project (2) for which you would like to revoke the Intercom connection. After the project page is loaded, select Project settings (3) in the left-hand menu, then scroll down to find and click on Apps -> Intercom integration. This loads the Intercom integration settings page.
If the connection is broken, the connection indicator (1) will be rendered in yellow and highlight the issue with a warning message. Click Reconnect (2) to connect the project to Intercom again. Refer to the documentation on connecting a Jira project to Intercom for further details on the connection steps.