How can I debug an AJAX error in VBO? (PDOException: SQLSTATE[23000]: Integrity constraint violation: 1062 Duplicate entry '' for key 'uri'
Duplicate entry '' for key 'uri' actually says a little more than AlexK realizes, it says both that there's a file without a uri, hence the '', and that you have more than one of these, hence the Duplicate entry.

I'm guessing there's a filefield on your users, and some of these have lost part of their data for reasons I don't understand. (The same thing happened to me once during a faulty export-from-one-site-and-import-to-another).

Why the process can be "forced" by repetition I don't understand, but close inspection of the user entity and any fields that could have a 'uri' key, both through devel and the raw data in the DB, should reveal what the source of the problem is.