Not sure what exact version of UCCX 7.x you are running, but if you are running anything less than SR5, Iw oudl consider upgrading. Your issue could be many things. UCCX authenitcate by passing through UCCX and using the AXL service to communicate and authenticate to CUCM and/or AD.
First make sure CUCM and UCCX versions are compatible via the compatiblity guide:
http://www.cisco.com/en/US/docs/voice_ip_comm/cust_contact/contact_center/crs/express_compatibility/matrix/crscomtx.pdf
Then do to desktop admin and see if you can run a manual desktop synch, if this fails, this will be a very good clue as to what is going on.
You could also try to restart the desktop services in Control Panel Services. I would restart - desktop Call/Chat and Dessktop Enterprise.
You could aslo try restarting Call Manager CTI Manager service on the pub and sub.
I am jumping around a bit because I really need to know more info to isolate things better and determine more about what is going on.