Getting Minification to show the list of available files

You go to Minification, click on Check Files, you see the progress bar. So far so good.

After a while you go back to check the Minification status - and the progress bar has disappeared, not a single file is listed, and you're back to square one, with the offer to Check Files.

Minification is not working for me - any ideas on how to make it work?

Thank you,
Alex