Thanks for pointing me to the thread.
It was long, as you said, but with little info of consequence.
I was using Tablets II until Talyns retired and then I figured I'd better switch to UI that's being actively maintained. I never had the chat window saving problem with Tablets II, and I was fortunate enough to have backed up my UI settings file before switching to TyeJae.
When I copied my old Tablets UI settings file back over much to my surprise, the chat window stuck.
Whatever the problem is, it is definitely in the UI settings file that causes that bug.