When you select a value the combobox makes a request to the server. Even if it is an Ajax request and the browser does not refresh, it is still handled as a full postback on the server side. This means that all controls will be recreated, including the captcha. When this happens, a new captcha image will be generated. The captcha image will remain only if the combobox does not make a full postback to the server.
the Telerik team