I tried uploading a index.htm file with a "Site being Updated" message and then I disabled the index.php file to see if that would have any effect.
Nothing happened. The new users were able to register anyway.
Most of the email address are from gmail or hotmail, and all have nonsense names, which makes me think it is a bot that is doing this on a regular, programmed basis.
Does anyone know how or why this is happening?