Hello,

1) This is most probably due to disabled History in your Firefox settings.
There is bug in Firefox that prevents add-ons from accessing database if your Firefox / Settings / Privacy & Security / History - is set to "Never remember history".

2) Or your Firefox has broken database support. This happens in some rare cases usually on very old Firefox profiles or for users that downgraded from Firefox 57.
To validate that you can visit this demo page:
http://mdn.github.io/to-do-notifications/
This page is using same database technology as my add-on. Check the log text in bottom left corner - if you see there "Error loading database" then your Firefox has indeed broken database.

What should help is Firefox reset feature:
https://support.mozilla.org/en-US/kb/refresh-firefox-reset-add-ons-and-settings
Resetting profile will preserve your passwords, bookmarks and other important things.

I hope this helps.

Have a nice day :)