Please check the Editor.ChangeAbsoluteURLsToRelative Property.
By default Internet Explorer converts all URLs in hyperlinks (anchor tags) and images (img tags) to absolute URLs. When this property is set to true (the default), CuteEditor strips out the local server name from all A and IMG tags if the hostname in the URL matches the current hostname.
In your situation, please set this property to false.
asp.net Chat http://cutesoft.net/ASP.NET+Chat/default.aspx
Web Messenger: http://cutesoft.net/Web-Messenger/default.aspx
asp.net wysiwyg editor: http://cutesoft.net/ASP.NET+WYSIWYG+Editor/default.aspx
asp wysiwyg html editor: http://cutesoft.net/ASP
asp.net Image Gallery: http://cutesoft.net/ASP.NET+Image+Gallery/default.aspx
Live Support: http://cutesoft.net/live-support/default.aspx