The RadCaptcha control changes its code on every trip to the server, no matter if its full or ajax postback. This cannot be overridden, because of security reasons.
You can create your custom captcha validation, based on our RadCaptcha component. A custom handler should be implemented to serve the image. Then you can create new images based on the fact whether ajax or full postback occurred.
I have attached a sample project showing how to implement a custom httpHandler.
the Telerik team