J! 3.3.6 seems to work fine (at least with Fabrik 3.2). However per the release notes:
Because of the issue with the update component, users who are running 3.2.6 or 3.3.5 will be unable to update to the next release using Joomla's update component. These users will be required to update their Joomla! installation via the Extension Manager. Instructions for updating via the Extension Manager can be found on the Joomla! Documentation Wiki. Users who are running Joomla! 3.3.0 through 3.3.4 and 3.2.5 or earlier will be able to update using the update component.
... so if you try to use the update button over those version you will get a login error. You have to use Extension Manager as indicated for those. The latest Fabrik is 3.2, so if you updated a couple of weeks ago that is what you should have, but can check in extension manager's version column.
