There are 3 possible reasons:

1. Captcha is not enable in the Module paramentes;
2. It won't show if the user is logged in, because if he is logged in there is no need to verify whether he is a robot or human.
3. Ajax Contact and Ajax recommend's Captcha feature only works with the MathGuard Library.The other libraries use server sessions which are killed once the form is submitted, therefore the user wouldn't be able to use the form again (if required) without reloading the page.