Mail Fails To Connect In My Office Network, Works on Reboot

This is baffling me and my network admin:

Mail fails to connect to any of my accounts at work. But it recovers if I reboot my machine.

Here is what happens:

- Mail works just fine at home. Connects to gmail, iCloud, and a 3rd party email account no problems.

- I get to the office

- I log in to the office WiFi with my password - for this I have to open a browser window, and enter my credentials.

(I kind of assume that this is the problem ^^)

- All my internet connections work fine, I can use the browser to access Gmail etc

- Mail refuses to connect to any of my email servers, and all accounts go offline

- Connection Doctor says "Mail can connect to the internet" but all individual connections are red, not reachable. I checked "detail" too - its empty.

Then I reboot my Mac, and after that everything's happy. Mail connects to my accounts normally, and Connection Doctor marks all as green.

Since it works on reboot, we can rule out network problems like closed ports etc. So the only thing I can think of is that Mail initially tries to connect as soon as I am on WiFi, then hangs (because I am not logged in yet), and somehow this hang is of a kind that does not recover (I've left it on for hours at a time, no difference, it never recovers).

Anyone have any ideas about this? Is there some way I can restart networking daemons to kill the hung connections. Or any other way I can diagnose this?