You have two emails on the page, but only one checks to see if it passed reCaptcha. You should wrap both in the reCaptcha check so that no email gets sent when the captcha fails. Then you can give the error when it fails to prevent people from thinking it went through.
Now you could also try to fix the issue with the captcha expiring after 3 minutes, but I think you should fix the issue that the captcha test doesn't actually prevent the second email or redirect as well.