By far the most common cause of a consistent failure to connect to Typekit is a bug in the CCLibraries process. The CC Libraries team is aware of the problem and an update to the Creative Cloud Desktop app (of which the CC Libraries process is one part) is in the testing pipeline for release.
If killing the CCLibraries process and relaunching Muse, or restarting your computer (which is just another way to kill the process and relaunch Muse), doesn't enable you to access Typekit, then we need more details regarding the exact error(s) you're encountering. Screenshots would be very helpful.