Can you confirm if telephony on UCCX pub is partial or out of service as these are two different things. Partial would mean some CTI ports or route points have config issues which can easily be verified by logging into UCCX RTMT>Click on "Cisco Unified CCX" button located at the bottom left corner>double click"CUCM telephony data">Double click "Summary" and check for any errors reported for UCCX pub.
If telephony is out of service on pub, then it would mean the CCX engine cannot communicate with the CTI manager(CUCM) properly and none of the calls would work. A starting point would be to restart the CCX engine service on the uccx pub.
