I'm dealing with the same issue at the moment myself. It's likely a jQuery conflict with another plugin/theme. However, even though I've reverted to a default theme (I've tried 2012 and 2013) and deactivated all other plugins, I'm still having the same issue. My current work around is to eliminate the spinner (for now) by adding this to wp-config.php:
define ('WPCF7_LOAD_JS', false);
I'm devoting the weekend to solving this issue, as I've yet to find a definitive answer.