Hi rain coaster and fellow members who just posted:
I don't mind if it's no longer working and I need to have the name servers on WordPress [dot] Com. There are two things here:
CloudFlare Support says everything is OK on their end - the name servers
I can issue a Ping command to my website and it sends packets of data OK.
If WordPress is running some flavor of LAMP - which I suspect they do - then they just need to query the Apache error logs for particular IP addresses in question, to see what the issue is.
What I'm looking for - if not a fix - is a reasonable and plausible explanation why this CloudFlare / WordPress combination is no longer possible. Name servers are not rocket science to software engineers, if you understand them. I used to interface with them on the Motorola Intranet, when I managed Apache servers and Oracle databases for engineers. You can read about them on Wiki at http://en.wikipedia.org/wiki/Name_server.
So what I seek is knowledge. Something to this effect: "This is no longer possible on WordPress side because (A) or (B) or (c) - whatever.
A word to the moderators. I'm not adding anything here, but just responding to the previous posters.