We have been seeing a strange problem on our site where the ‘ReCaptcha’ challenge was not always being displayed when it should have been. Most notably this is/was seen on the site registration page, but was not just restricted to that page. A complete page refresh often resolves the problem and shows the Captcha block.
We today saw that a change is proposed for the next Joomla update. It is mentioned in this post from OSTraining, which in turn refers to the fix itself which is extracted from this joomla.org doc.
The basic problem seems to be that Google changed the URL’s of the Recaptcha API location, which doesn’t completely explain what we are/were seeing, but implementing the fix cannot do any harm and may even resolve the problem.
We will watch it for a while and see whether it completely solves the problem, but recommend it is implemented on your sites if you are experiencing ReCaptcha problems. It does require FTP or SSH/Telnet access to change the plugin code.
Update 29/11/2013: Doesn't solve the display problem, so still investigating.