Redisplay Captcha on form error in Ajax form submit
If user can submit the form when there is no captcha after errors, it's by design. In captcha settings you checked an option to only verify humanity of an user once. User gets validated as a human on first, failed submit, and is not bothered any more on that form. Go to captcha settings and make him validate each and every time and it will not disappear, but your users will not love you.