Thread:Extension talk:WYSIWYG/WYSIWYG works by IP but not by URL/reply (2)

This is not problem of wysiwyg. This is either problem of your MW or DNS. To me it sounds like DNS problem. Could you try commands: ping 10.10.10.123 and ping wiki.specialdomain.com or nslookup wiki.specialdomain.com

Do all respond?... if not then it may be DNS problem.

You could also check how you have setup your wiki in LocalSettings.php: "$wgServer = ...."