I can't link with CQ using Internet Explorer 9
One answer
Do you have Quality Manager and ClearQuest both configured to use http, or both configured to use https? The symptom described sounds like you may be experiencing the behavior described by this techonte:
http://www-01.ibm.com/support/docview.wss?uid=swg21586892
http://www-01.ibm.com/support/docview.wss?uid=swg21586892