Hi all, thanks for all your help! Logging in and out helped
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If you're using Google Chrome, I've found a fix: (It'll also work in other browsers, you'll just need to modify the instructions to find out where you can delete site data and cookies)
Go to chrome://settings/
Search settings for "cookies" and then click the highlighted content settings, and then cookies
then click "see all cookies and site data"
then where it says "search cookies" type catanuniverse
then click the delete on all of the search cookies things
Now, you'll be logged out and able to log back in, and it'll be in online mode
Just tested now, December 5th 2017, on the latest version of Google Chrome, and it works great.
Workaround: fire up the game on both your mobile device and your computer. Doing so will log you out from one of the two devices, you'll then be able to log back in the other and be online again. You can only be logged in one device at a time.