It's one of the downsides of web IRC clients like Mibbit, different servers might limit the number of connections allowed by the client. You can try and try again until it works, the widget tries a different server each time (or most of the time) you try to connect. Else, you can try a different client, you can find plenty of them on the interwebs.
http://en.wikipedia.org/wiki/Comparison ... at_clientsI personally use mIRC, an old habit I developed more than 10 years ago, but it's not necessarily better or worse than any other. Once you get a client, connect to Undernet and find us on #fof-ff (or open this link with your client:
irc://us.undernet.org/FOF-FF ). Good luck