I can’t say exactly what makes this happen, but there is a workaround.
I’m assuming you’ve built and rigged each character in its own file and that you’re Appending the two characters into a third file where you’ll be animating them.
Open one of the original character files and click on any part of the rig so you can access the Properties window’s Rig tab.
Near the bottom of the Rig tab, find the Custom Properties panel and look for the rig_id variable.
Select the value of rig_id, and copy (using Ctrl-c).
Now close that file and open the other character’s original file and replace its rig_id (Ctrl-v) with the one you just copied.
Then open the Text Editor and click on the notepad icon beside the New bottom. Find the rig_ui.py script and select it.
Go to the top of the script and find the line that reads:
rig_id = “whatever_the_rig_id_is”
Select the part inside the quotes and paste in the rig_id from the other file.
Save a new copy of the file.
Now you should be able to Append both characters into a single new file and, after setting up proxies for both, you should be able to go back and forth between them without trouble. The UI will always be there.