This needs to be a catchy name, but I don't have a good one. CloudFlaritis? CloudFlareup? (CloudFlareDown?)
Regardless of whether Cloudflare is the particular infra company, the company who uses them responds to blocked people: "We don't know why some users can't access our Web site, and we don't even know the percentage of users who get blocked, but we're just cargo-culting our jobs here, so sux2bu."
The outsourced infra company's response is: "We're running a business here, and our current solution works well enough for that purpose, so sux2bu."
I'd say Clownflare, but that sits too close to Clown Care, who do really great work.
Hmm, "cloudfail" is already in use, and "cloudfuckyou" while descriptive is profane enough that it will cause unnecessary friction with certain people, and "clownflare" is too vague/silly (and is less applicable to other service providers).
So I propose "cloudfart" - just rude enough it can't be casually dismissed, but still tolerable in polite company. "I can't access your website (through the cloudfart |, it's just cloudfarting at me)."
Other names (not all applicable for this exact use): cloudfable, cloudunfair, cloudfalse, cloudfarce, cloudfault, cloudfear, cloudfeeble, cloudfeudalism, cloudflake, cloudfluke, cloudfreeze, cloudfuneral.