IPad 4 iOS 6.0.1 cannot connect to Facebook

Question

Hi all,
I have a strange problem that I'm trying to solve.
I have an iPad 2 (iOS 5.1.1), iPhone 4S (iOS 5.1.1) and now an iPad 4 (iOS 6.0.1)
Using the WiFi network at work the new iPad cannot connect to Facebook properly. The two older devices, on iOS 5.1.1, connect and work without any problem. (please read on, it gets stranger!)
Some more details:-
The old iPad and the iPhone can connect to Facebook fine, using either the Facebook app, Fera or Safari or Mercury browsers.
The new iPad "sort of" connects - I can access settings, user icons in the RHS chat bar update and are correct, but it cannot update the newsfeed, no new posts at all and after 30 seconds or so, a red bar saying "Network unavailable" or similar.
Fera is the same, settings load and work, user icons work, viewing my home page seems to work, newsfeed - nothing updates.
Using Safari it seems to load OK, but the "this page is still loading" progress indicator carries on, and on, and on, and on. Using Mercury browser and the same thing happens, plus after a short while Mercury actually tells me that it couldn't load the page. No newsfeed updates at all.
If I disable WiFi and enable 3G data, it works no problem.
If I'm using my WiFi connection at home, it works no problem.
I am the network administrator at work and the WiFi is an unfiltered, unblocked, unfirewalled connection. (it has an external static IP which goes through NAT and then to two WiFi access points and one DMZ PC) The ISP is a business account at Easynet. I'm not aware of any port blocking that they do, and even if it was port blocking further up the network, it should affect all my iDevices, not just one?
The fact iOS 6.0.1 has problems and iOS 5.1.1 does not suggests to me it's a problem with iOS 6.0.1, but the fact it works fine through 3G and my home WiFi connection suggests it's port blocking at the work connection.
I suspect either the new integrated Facebook in iOS 6.0.1 is connecting a different way to iOS 5.1.1 Facebook (and ditto for the browsers!) or maybe SSL over port 443 is being used and is different somehow between iOS versions?
I've checked the iOS logs (using System Status app), nothing of relevance there. I've checked the network connections and nothing out of the ordinary there (but if it tried to connect via a blocked port, it would fail and not be listed in the port list anyway)
Is there anyway I can log all (successful and unsuccessful) network connections that happen (for everything)? I do have an Apple developer account, is there anything available there I can use to track the problem down? (I've just registered, haven't gotten round to doing anything with it yet so I'm not aware of what's available in there yet)
I've tried:-
Deleting and reinstalling the Facebook app (but as the Facebook website also has problems I didn't expect this to do anything, and it didn't)
Hard reset of the iPad.
Putting the iPad into DFU recovery mode, letting iTunes completely reinstall 6.0.1 and setting it up as a new iPad. (no restore)
Nothing has made any difference.
I've had the iPhone and new iPad next to each other, 3G data disabled, WiFi connected (to the same access point), iPhone works fine, new iPad doesn't.

Answer 1

Mine has never worked right for more than a couple days, then it just stops.  I don't even try to fix the thirty things that don't work on my junk iPad.