There are probably many things that could cause this issue. We had a similar issue where we couldn't save changes to the primary UCCX server, only to the secondary. We found that the CCX database service wasn't running on the primary. Not sure if you have a simliar problem but maybe worth ruling out.
Thank you all for your helpful replies. It was DB related, in that a co-worker was testing some custom reporting and had populated the db w/data from another cluster - as this cluster is not yet in production. Even though the CSQ's were not visible via the web admin, they indeed existed in the db. So you can say the root cause is "communication" related.