If the issue can't be solved, at the very least, the CAPTCHA page should have some text pointing this out or directing people to a workaround. It's pretty terrible UX to just keep a user blocked out while saying "Oops! Those aren't the correct words."
OK, the source of the bug appears to be this code block in Area 51 HTML source code for the captcha page:
Since Area51 moved to https, this now cause a "mixed content" error in modern browsers.