"Check Availability" on new user/member form fails silently while "Checking.."

On Wordpress 3.8.3 (multisite) and CiviCRM 4.4.4, I created a Member Signup form (viewable at: http://studentleadership.ca/membership/join/?page=CiviCRM&q=civicrm/contribute/transact&reset=1&id=2)

"Check availability" functionality worked just fine.

CiviCRM was then upgraded to 4.4.5, and simultaneously an SSL certificate was installed using the WordPress plugin: WordPress HTTPS with all pages forced to https.

I then noticed "Check availability" functionality on the new member signup page was no longer working. I can still force a warning message "Your username contains invalid characters" if I include bad punctuation in the CMS UserName, but if I enter a syntactically valid WordPress Username (existing or not), the "Checking..." shows constantly and no response appears to come back (i.e. silent fail).

I then removed HTTPS from the site so all pages show as http, and got the same "silent fail" behaviour. Note that "Remove Unsecure Elements" in the WordPress HTTPS plugin is not selected.

I took a look into the code and it appears the code sequence has had a number of changes in the last 2 releases. Is this a new bug?

I cannot test this fully in "CiviCRM WordPress Demo Site" as WordPress Register New Users is turned off. However, I modified the WP Member Signup form there as close as I could to the setup of my install. If someone could turn on "WP Register New Users Allowed", you could check this at:
http://wordpress.demo.civicrm.org/?page=CiviCRM&q=civicrm/contribute/transact&reset=1&id=2