Once a student completed a discussion comment (DC) (the purple box), the current design is that the DC will be marked as complete, and should appear in the tutor's inbox. Once they read it, however, it leaves (once it's read it won't appear in the inbox again).
There may be issues with the current implementation not marking the comment as unread, and the tutor never seeing the response, so the task remains on to discuss (because the tutor never marks it).
The change would be to have a completed discussion comment (a student responded) to always appear in the tutor's inbox regardless if it's read or not because it's an action the tutor needs to take.