Thank you for the additional clarification. Would it be possible to confirm if you are using SSL? Also, are there any errors in the Console window when refreshing the page with FireBug or Chrome Dev Tools open?
Could you please open the Web part properties and temporarily disable "Check Permissions" and "Hide if no record found" if they are enabled?
Was this instance upgraded from an older version?
We are hoping to find way to reproduce this issue. If we are unable to determine the cause based on your answers to these questions, we may request that you send a backup of your project to support@kentico.com so that we could take a closer look.
Thanks in advance for the additional details.
Best Regards,
Sandro