Mine is actually a revamped twenty twelve theme. I also put twenty eleven up as well and both have the error still.
I updated this plugin and WordPress but I am still having that issue. I love this plugin too and use it all the time. This is a new error as far as I can see and isn’t happening on all sites that use Contact7.
My plugins are only: (all updated to the latest version)
Contact Form 7
Really Simply CATCHA
Ultimate TinyMCE
WordPress SEO
I am having the exact same problem. The arrows just keep spinning and there is no “Your message was sent successfully. Thanks.”. This only happens when CAPTCHA is used. Then users keep pushing send causing the message to be sent over & over again (spam).