It would be a heck of coincidence if it wasn't CCleaner since it only happens after a clean. I found quite a few articles on the Photoshop-specific problem in my research to try to ind the settings save location, but that's a much older version that has since been fixed.
Yes, just the "favorites" setting goes away, fonts stay just fine. Doesn't look like the possible folder was the right one either as they still disappeared...even tried excluding the whole Photoshop folder that was under, but no joy there either.
Tried the file list option and found a couple of temp files that were Adobe related and excluded them all. That seems to have done the trick. Next time I have a few extra minutes I'll go one by one to see if I can find the specific culprit and I'll report back! I still find it funny though that Photoshop isn't a selectable program option when Illustrator is, but it could be a version difference. My Illustrator version is pre-Creative Cloud so it's a bit more independent.