The one thing I've seen some sites run into with CloudFlare sounds like it could be exactly what you saw with that site (at least that's a symptom of the issue). Where a server is configured with its own DDoS protection or somewhere upstream at the network level the same thing. Like when someone hears, "Oh DDoS protection, good idea..." I'm But the admin doesn't configure it properly). Lol
So the server ends up seeing a zillion HTTP(S) requests for the same (CloudFlare) IPs and starts blocking the traffic to CloudFlare IPs because it thinks those IPs are attacking it.
On a side-note, anyone who's site is accessible via direct.domain.com really is just plain dumb if they don't want to be DDoSed for real.
That being said, I've been running every site/domain I own through CloudFlare over HTTPS for almost 2 years now... Billions of HTTP requests, and I've never had any issues myself. If some site get CloudFlare origin server errors, I'd almost bet money it's some anti-DDoS system they have in place that's kicking in because of poor configuration.
Also - the site you are on right now uses CloudFlare (xenforo.com). Do you see CF errors popping up here ever?