Make sure your firewall allows a connection to mIRC's Ident server. Depending on your computer's configuration it may mean just opening the port or opening the port and forwarding it if you are on a network. Having said that, not using Ident may not necessarily be the reason that you are banned.
On the face of it , this looks liek that the subnet you are using has been banned because some lamer has been redialling/reauthenticating to avoid bans placed on single IP's/hostnames. Emailing the admins of the network you want to connect to may yield more informtation on why you are affected by this.