Have you tried deactivating CloudFlare or possibly contacting Eleven2?
Also activating CloudFlare wouldn't cause the server IP to stop pinging (though, it may cause a domain to stop pinging). You may be firewalled. Try pinging your server IP here: http://cloudmonitor.ca.com/en/ping.php
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Yeah the best thing is contact them to do it, however if they are slow that sounds like hell. But that's not Eleven2's fault it's the Cloudflare side of things. Sounds like something is mucking up from Cloudflare to the E2 cloudflare plugin. Good luck resolving it, if you don't get a reply I'd recommend moving.
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Well once again I am suffering the slings and arrows of misfortune.
As of yesterday I deactivated cloudflare and today I am still seeing connectivity problems with the websites even though they said that they unblocked the ip.