This issue is resolved in 9.1 versions and up. If you are unable to upgrade, use the workaround listed below.
In the file ~\Workarea\captchaImage.aspx.cs, update the Page_Load method to set AllowAnonymous = true; as the first line. For example:
protected void Page_Load(object sender, EventArgs e)
{
AllowAnonymous = true; //original code goes here
}
This change disables authentication for this page. As a result, the captcha image will appear regardless of logged-in state.