Why won't data entered into CiviCRM profile html snippet save?
I wonder if it's the recaptcha on the form action page?

http://tremololabs.com/clients/IREHRTEST/index.php?option=com_civicrm&amp;task=civicrm/profile/create&amp;gid=15&amp;reset=1

My guess is that posting to that page without the recaptcha data (which is what your form does) is going to cause the server to be annoyed, and perhaps there's some kind of code or server security something that is hiding the response and just sending the user to the front page of your site? Do you have some kind of special configuration for your recaptcha perhaps?