I'm sorry that you ran into trouble with this! The next time that you see this problem happen, please try turning off font sync in the Creative Cloud application, wait a moment, and then turn it back on. The option to do this is under the gear icon in Preferences > Creative Cloud > Fonts ("Typekit on/off").
That will start a new sync session, and should get the fonts working for you again in the short term. It's a workaround, but will be faster than removing the font from your sync selections and adding it again.
Then we'll need a little more information to determine why you are seeing this issue to begin with.
The next time that the fonts stop working, please:
1) make a note of the time by the computer clock as soon as you notice.
2) turn font sync off and on again; or do whatever else is necessary to get them to sync
3) make a note of the time by the computer clock again
4) send us the two times and the new sync log from the day that you run the test at firstname.lastname@example.org.
Instructions on where to find the log files are here: https://helpx.adobe.com/typekit/kb/troubleshoot-font-syncing.html#logs
Our engineering team would like to check the events in the sync log against the timestamps, and try to get some more details on what is causing the behavior that you're seeing.
Please let me know if you have any other questions in the meantime, and thank you for your help! Best,