In order to stay notified of recent posts on a discussion, the Notifications option is helpful.
Note: New post notifications will be sent to the user's external/institutional email address, not via the Messages tool.
Select the Discussions tool from the Tool Menu of your site.
Select whether an email is desired for whenever a new message is posted on the Discussion, for every new message posted on a conversation that the user has contributed to, or to simply turn off all notifications.