Are you using WordPress as the SSO provider for Discourse? If that is the case, when you logout of WordPress, you should be also logged out of Discourse.
If you would also like to have it so that when you log out of Discourse, you will be logged out of WordPress, you need to add a URL to the ‘logout redirect’ setting on your Discourse installation. The URL should be set to example.com/?request=logout
This needs to be better documented.
Can you double check that logging out of WordPress is not logging the user out of Discourse? I haven’t heard of any problems with this since it was implemented. It works correctly on both my development and production sites.