I tried writing to Cloudflare and they kindly replied:
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From: Jeremy
Subject: Is this correct?
Hi Jill,
Thank you for contacting CloudFlare.
susans.org currently has over 750 concurrent users. To keep the service running smoothly for all users, we limit the maximum simultaneous connections to 750 for a single domain. This is why you're seeing that error.
This cannot be altered or overridden. I apologize for the inconvenience.
Let us know if you have any other questions.
Now that I have finally managed to get in, using a proxy server suggested by our own dear Cindy, I don't think this is actually true. The number of visitors here is not 750.
I confess I did get a bit worried that it was only me. OK, I know that sounds terribly self centred, but I'm an introverted, neurotic, middle aged women who spends most of her life living a lie. Sometimes I need to think about me.

I think the problem is a bit more serious than simply cloudflare. They claim to exist to stop DDOS attacks, yet this sounds exactly like just that.