It appears the CAPTCHA is working... you just don't have a success redirect, so it is hard to tell the difference... however I'm pretty sure the registration email isn't sent unless the CAPTCHA is correct.
I think the changes you need to make to allow this to work more smoothly is to add a success or failure message to the very top of the form and add validated form bindings to the existing fields so they maintain their values when the CAPTCHA fails.
I've gone ahead and made those changes for you... Please download the updated file I've made the additions to.