Hi,
Please try to disable the publishing feature to check whether it working or not. Or try to restart Distributed Cache service.
If you do not activate the publishing infrastructure feature, the note board will appear to work, but will not store comments correctly. The note board does not use the correct url for the page, so the notes stored using the web part, will differ from
the notes stored using the Tags and Notes button.
https://donalconlon.wordpress.com/2011/03/02/adding-the-social-note-board-to-a-sharepoint-blog/
I suggest you activate the publishing infrastructure site collection feature, then add a new Noteboard web part in a page, then check whether the issue still exsits or not.
Best Regards