This could be a permissions issue. All the content items should inherit the permissions set for the page. Please make sure the content that is exhibiting the behavior has it's View permissions set to allow anonymous users. You do that by editing the page, select the More link for the widget and select "Permissions". "View a Widget" should be set to "Everybody" if you haven't changed it.
Please feel free to contact us if you have more questions.
the Telerik team
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