It sounds like you're not licensed for HA. Were you using a 60 day demo license? Or, were you issued a temp license from Cisco?
Login to UCCX Admin webpage and then, navigate to System > License Information. I believe, UCCX v9 displays cumulative license information as well. If not, select the most recent license file(s) for additional info. Check the following; Package type (i.e. premium, enhanced or standard) and High Availability (i.e. Enabled/Disabled). The Package type must be Premium or Enhanced. The HA feature is not available on the Standard license. Needless to say, High Availability must be 'Enabled' as well.
Did you recently change (update) one of the following system settings; IP Address, Subnet, Gateway, Hostname, TZ, SMTP, DNS, NTP, NIC Speed or did you generate/regenerate certificates on your UCCX servers. If so, this directly impacts the License MAC on the UCCX server which is used by licensing. If you changed something, UCCX would automatically generate a 60 day temp license. Most likely, you would've noticed the "temp license warning message" when you login to UCCX Admin webpage.
If everything appears to be Ok with the license(s), then I would check the status of the UCCX services. Navigate to Cisco Unified CCX Serviceability > Tools > Control Center - Network Services. Check the status of each service. Do you notice any problems? If you can, perform a failover... does the Subscriber node assume the [M] role? If not, is there one or more services displaying "partial service" or "out of service" on the Subscriber node? If so, which services?
Next, you can check/compare the configurations on CUCM and UCCX.
Login to the UCCX Admin webpage > System > Cisco Unified CM Configuration. You should have two CUCM servers (CTI Managers) as the CM Telephony Provider and RmCm Provider. Verify the configurations exist on CUCM as well. You should have 'Application User' accounts that correspond to these accounts, however, I believe you would've received a different error message.
Additionally, check the configurations under Subsystems > Cisco Unified CM Telephony. Click on the "Data Synchronization" and check the boxes, then click on the "Data Check". This only checks for inconsistencies within the Call Control Groups, Triggers and CM Telephony Users between the nodes. Click on the "Data Resync" if you wanna... well, resync the data. Likewise, JTAPI might become out of sync after upgrades, s/w updates, etc. From my experience, this only happens during major upgrades - like upgrading from v8.5 to v10.x or whatever.
We have seen this issue crop up a couple of times in our UCCX environment. We are running UCCX version 10.6(1)SU2 in HA. We have significantly more licenses that we have users on the system. This very problem happened to me this morning and has happened in the past. In all of my internet searches I didn't find any reference to what we have done to fix this issue each time. This is what I did to fix it.
Log into the Cisco Unified CCX Serviceability page
Navigate to Tools -> Control Center - Network Services
Find the "Cisco Desktop License and Resource Manager Service"
Restart that service
In the cases where we have seen this "A licensing error has occurred. Please try again in five minutes" error when agents attempt to log into UCCX using the Cisco Agent Desktop (CAD) software, this has fixed the issue. Of note, we haven't made any changes to our system recently. It appears that for whatever reason this service can get hung up. Looking at the service in Control Center gave no indication that there was an issue with it. It still showed a Status of "In Service."