Closing a comment thread is used to halt the discussion while allowing the current comments to remain visible. Closing comments can be done several ways:
For your entire site you can specify how long you want comments to remain open after the thread has been created. You can find this option in your Disqus Admin > Settings > Moderation Settings page under Automatic Closing.
Note: You can override this length for individual posts by going to the page directly and clicking the Settings gear to change the option.
Manually closing from the thread
To start, make sure you are logged in to your Disqus account. While viewing the Disqus comment section of an article, select your name on the top-right to trigger the Settings dropdown and then select Close Thread.
This method can also be used to re-open closed threads.
Manually closing from the Discussions tab
Manually closing from the admin
To close a thread in the Disqus admin:
Locate a comment that belongs to the thread.
Expand the comment.
Click the Discussion menu.
Choose Close Discussion.
Using the WordPress plugin?
Disqus will respect the Wordpress settings with regards to disallowing commenting. If you're using Wordpress, you can remove Disqus on a per-post basis by disabling comments for each post in WordPress itself, or setting an Automatic closing timer in your Wordpress discussion settings. See WordPress' Enable and Disable Comments guide for steps.