I have the same problem on almost all a321 flights. In fact I'm having it now on the BOS-LAX flight!
I can rarely get any websites to load on my laptop on the a321, except sometimes the BBC. It says I'm connected and info on the flyfi page does get updated like flight status.
Everything works when I use my iPhone.
Any ideas for how to get my laptop to work? I tried reconnecting to the network, restarting the computer, and even installing the windows updates that have been promoting me for a couple weeks just in case.