No HTTPS?

function recaptcha_get_html ($pubkey, $error = null, $use_ssl = false)

However, use_ssl is never passed true. When switching your site to https, browsers block the request to Google, and you can lock yourself out of your blog.

I had to change the default of $use_ssl to true.

https://ww.wp.xz.cn/plugins/wp-recaptcha-integration/