What I do is, for the few threads where I think it's useful, I keep a browser tab open with only the specific thread I want to watch (click on a comment's timestamp to open only the thread below that comment).

Alternatively, you can use the second menu item "Threads" for an easy overview over all your comment threads including replies to your comments.

This also has the advantage over notifications that you decide when to look at the discussion, instead of waiting for notifications (immediate discussion thread notifications - a great evil of our time).