You could try disabling any anti-virus or firewall software to see if that helps.
You could also try downloading mIRC again from the mIRC website and installing it in a different folder and using the "portable" option in the installer (so that it does not overwrite your current settings and scripts). Now try connecting with this copy of mIRC. If that works, this may indicate that a script is causing the issue.
If the issue persists, and you are able to connect to other IRC networks without any issues, this may indicate that the IRC network is not allowing you to connect for some reason. You would probably need to contact them through their website to see if they can help.
