Cloudflare is a large business devoting many resources to detecting and blocking 'undesired' traffic and many large sites use it. I assume they have all the same tracking capabilities as the major ad platforms, and can detect the difference between an automated program like FFF and a real browser. Were you doing a lot of downloads/updates when the problem started?
I've just now downloaded another story update from SB without problems, so I continue to believe it's not a universal issue.
I don't believe SB/etc are sites I've put any effort into testing BrowserCache with. A quick look now shows page response from SB marked no-cache by the server, so I wouldn't expect it to work.