We just upgraded to reCAPTCHA 2 in the latest release. I’d recommend first following Google’s instructions and register a new key:
https://www.google.com/recaptcha/admin
It may be a JavaScript conflict on your site – if you’d like support just open a topic on our members forum so Jason and Jess can look at your unique issue:
http://www.paidmembershipspro.com/forums/forum/members-forum/
I get similar issue after upgrade …
Fatal error: Cannot redeclare class ReCaptchaResponse in /home/user/website.com/wp-content/plugins/paid-memberships-pro/includes/lib/recaptchalib.php on line 37
Reverting back to previous plugin build fixes the problem but cant use the latest recapture.