Disappearing UI is a new one to me. What OS / hardware specs is this happening on? Is the puppet or scene you were working on particularly complex / resource-intensive (low framerate, moves slow)?
Usually projects get saved by default in your Documents folder under Adobe > Character Animator. Is your previous project showing up there, or did you save it in a custom location? Was this on a local drive or an external one?
Does going back a few steps in the history panel help anything? Can you isolate a particular step where everything went wrong, and if so, what was it?
Answering in order:
OS X 10.12.4 (16E195)
Mac Pro (Late 2013)
3.5 GHz 6-Core Intel Xeon E5
The Puppet is the Maddy demo puppet from Athena Studios. I was animating a scene with 3 characters by recording the first character's performance, then dropping the scene into the timeline of the second character's scene so as to have reference of the scene composition, and so on for the third scene. It seemed like a simple work around, and similar to pre-comping in AE. Perhaps this is not an advisable method?
The project is saved in a custom folder. However, even after opening the custom project file, the program continues to refer to the project as "Character Animator Project 3", which is a different -- currently empty -- project under Documents > Adobe > Character Animator. All files are on the local drive.
Going back two steps does appear to have fixed the disappearing UI problem, but not the above mentioned project name issue. At the time the issue occurred I was deleting extraneous audio takes.
If you do File > Reveal Project in Finder, does it select the project folder you're expecting? Note that the name of the project is considered to be the name of the folder that _contains_ the <name>.chproj file, which is actually just a dummy zero-K file so you have something easy to double-click on.
After Stepping Back in the project to a time before the issue like Oksamurai and then subsequently closing and reopening the program, the issue with the project name seems to have gone away.
So the problem was reversed by:
-restarting Character Animator
However, the bug is replicable: Trying to delete audio takes in the timeline causes the labeled layers to the left of the timeline to vanish.
Can you reveal the project in the Finder, archive the project folder (the folder that contains the .chproj file and Ch Data and Ch Media subfolders), and the share a link to that archive via Dropbox, Google Drive, etc.? You can send the link via private message if needed.
I also had a problem with an "internal error code: Assertion failed!" everytime I tried to get into Rigging Mode. For me it helped to create a new project and import the old one.
Maybe this is worth a try if you have similiar struggles.