"Shop" mogs continue to wipe themselves at log out ~40% of the time. Is there a fix?

It is a very known and very well-documented bug. They are working on it, as they have been since it first broke in June with the release of 9.1. There is currently no fixes or work-arounds.

You have the mogs that you paid for. Unfortunately they disappear from being mog-able with no rhyme or reason, just as they’ll reappear the same way.

You are welcome to request a refund for the Celestial mog, but that’s kind of it at this point until they figure out why this is happening to some people, but not all - and why it’s happening some of the time but not all of the time.