Please clarify whether the RadCaptcha image is grey or if there is no image at all.
The first issue (grey image) occurs when there is a problem with retrieving the stored code of the captcha control. This usually happens in a load balanced environment (web farm/web garden). If this is the setup in your production environment, I would suggest checking if you followed all of the steps in the linked help article and especially the third one: http://www.telerik.com/help/aspnet-ajax/captcha-webfarm-and-webgarden.html
If the image is not loaded at all, this could happen as a result of a problem with the WebResource HttpHandler that loads it. You can check if this is the case by using the developer toolbar of your browser to review for failed requests to the server. The developer toolbar should also help you inspect the error and determine why the request has failed, if this is indeed the case.
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