I am running CUCM 8.6.2 and UCCX 8.5.1 with the latest update from the cisco website, the serves "Cisco unified ccx engine" will not stay on. I restart or start the serves and it will go partial serves and then back to shutdown. I have seen on other support forms that ther may have been a bug that the CUCM replication serves was not playing right with UCCX. The workaround was to change the rmcm username and password in UCCX, then change the password in CUCM I have done this and it still did not fix the problem.
What exactly is showing as Partial under CCX Engine?? CM Telephony Subsystem, RmCm Subsystem or what. In case it is CM Telephony subsystem, launch RTMT for UCCX and then go to Cisco Unified CCX (bottom Left Hand Side) >> CUCM Telephony Data >> Double Click and check the status of your CTI Ports and Route Points.
It will go down the list and start all the sub serves and before it can get to the end of the list it will start to shutdown from top to bottom. I was not able to find what you were asking for in RTMT but the 2 RTMT pics is what i was able to see. CTI ports and route point in CUCM are unknown and unknown and are not registered.