I’m having the same problem after upgrading a site to WordPress 3.7.1. Now, after clicking ‘Add Media’ and selecting an image, the box / field for adding tags is no longer there.
However, if I select an image and then click Edit, the Media-Tags box does appear to the right of the resulting ‘Edit Media’ page – so the plugin is active and otherwise working.
I don’t see any error warnings in the settings or role managment pages.
Hope there’s an easy fix. Thanks.