I had this same problem a while ago. I honestly don't know a solution, as I didn't do anything to fix it, but it started working again after 3 or 4 days, so at the very least I don't think you'll have a permanent problem with it.
Are you just unable to connect to a certain realm? I was able to connect to the other 3, just not the one I usually got on, and it worked for other Blizz games like D2 or SC.
Are you on a router? Have you tried reseting your modem/router? Refreshing your IP? I wasn't really concerned with it when it happened to me, as I rarely actually use b.net, so I didn't try these, but might be worth a shot if you haven't already.