I was wondering what it was when it popped up on NoScript a week or so ago, but I never allowed it.
It's not really a question of allowing a script, though there are some scripts that are bundled in with it.
Cloudflare basically serves up a cached version of the site to everybody. This speeds up performance, serves up the cache from a server closer to you physically, provides additional security measures, and a few other things. It's not simply a script, it's considerably more involved than that.
I'm keeping my eye on this and have only experienced it once. I noted that hitting the retry button got me to the site just fine that one time. I'll need to see if there are any downtimes in the server logs (cloudflare checks out, and well, if you saw that screen then cloudflare was working just fine).
The only thing I can think of is perhaps latency- do you all know exactly what the URLs are that you are trying to access?