I believe you would need to delete your post if you insisted on using this specific feature.
An alternative is to use the 'watch-list' feature (which is right below the new replies to your posts link) and you can easily remove threads you no longer wish to "watch" by clicking on 'edit watchlist' and deleting the threads that no longer interest you. I believe that all threads you post on will, by default be added to your watchlist
I know that but I have made over 530 posts. Just searching posts and deleting them is a head-ache. Really, the legendary members might be pissed out for making so many posts.
If you click on watchlist, you should see threads that have new replies to them that you have not looked at yet. When you click on your watchlist and see something you no longer want to see copy the thread name, click on edit, then use the "find" feature on your browser to find the thread and delete it.