I was able to recreate the problem using Safari for Windows. Something is non-standard or buggy with the release of Safari for windows that I'm using (the latest from Apple), and that seems to be the root of the problem. Safari appears to be neglecting to send the proper request instructions with the image requests, and the website doesn't know you are logged in for the images.
I put a work around in place to keep the annoyance to a minimum - you shouldn't get any more prompts on the pages with thumbnails, but it may still prompt you when you view a large image or movie. Be sure to check the "remember" checkbox, and you shouldn't have to keep re-entering it.
Please let me know if you are not on Windows, as I couldn't re-create in OSX.
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