So after a long email conversation back and forth it seems for us the issue is network related. Some where down the line before you get to WP's servers provided by provider Peer 1 the connection gets refused.
If you do a tracert from the server in question or from the client (depending on who can't reach WP), you'll notice that the ip address changes about 3 times (do the tracert more than once), this is what I believe is WP's load balancing cluster (nginx).
I found two of the three IP addresses reject my incoming request, but the third will let me in and post via xmlrpc, making it like Russian roulette. And of course if you get the two addresses that reject, you have to wait until the DNS lookup expires to try again (from your browser).
What I did to patch it so to speak was use our host lookup file in Ubuntu (server edition) and route our blog to the one address that works. Although this kinda duct tapes the service together, it will work.
Unfortunately for a lot of bloggers, you may be using a shared hosting plan, which will not give you access via SSH to change the hosts file. You might have to contact your help desk to see if they can fix the issue for you.