I'm pretty sure that this is a code bug in WordPress.Com. WordPress seems to revert back to a previously saved state, just by logging into the custom fonts panel, even without changing or saving anything.
What you described shouldn't happen and does sound like a bug.
I've only seen one other similar report where someone said they could save font changes but the settings were reverted any time they made a new change to anything in the Appearance > Customize section.
First, I'm working to test this in my own test blog. I changed my test blog theme to Chunk, selected some custom fonts, saved, viewed the front end to make sure the save worked, then went back to Appearance > Customize > Fonts and selected the default fonts again. So far, the fonts are stable for me.
Since I haven't been able to reproduce the problem in testing so far, would you be willing to try a test on your blog for me so I can document the issue?
If yes, please go to Appearance > Customize > Fonts in your blog dashboard and change the fonts back to default and let me know in a reply here as soon as that's done. After the change is made, don't make any other changes in Appearance > Settings for a few hours and then let's check it again at that point to see if the font settings get reverted or not. During this test, could you keep a general log of any changes you make to the blog? I want to see if saving something else is triggering the fonts issue for you even though you think it seems to be changing randomly.