Excellent suggestion, Mofi, to check if the taglist file is write-protected. It isn't, though. I've checked it. I should have thought of that first, though. I'm slipping.
The active group being stored on exit explains why I have to exit and come back in for it to work. Funny though, apparently it doesn't store it if it is "hidden" while docked. I have to make sure it is not "auto-hide" and "undocked" before it will save it on exit for me. Perhaps UltraEdit has a problem remembering to save it if it isn't visible.
I was having problems with my email server (my ISP was, at least, therefore I was too) so I was unable to send out the bug report until yesterday evening, but it has been sent now. I'll just wait and see at this point.
EDIT: I've heard from support, and they were able to reproduce the issue as well, and will have the developers look into this issue. Hopefully, it will result in a bug fix upgrade soon.