When I originally tested the problem, I saw that issue too. However, I saw similar behavior on the main Joomla admin panel page with the sidebar menu option for "Searching for updates.." It hangs there too. It seems like something with how Joomla performs the update is throwing a PHP warning, which is breaking the AJAX request.
Try on the admin panel page to see if that breaks for you too. If so, there's little we'd be able to do to fix it, since we're just calling the Joomla update logic as well.
Thanks,
Alex