There are 2 standout issues with the current webIRC (qwebirc) so I suggest a replacement.
Currently the webIRC needs Flash for sound notifications to work.
Using HTTPS fails. I have used qwebirc with HTTPS so I know it works.
I suggest a modern and very stylish webIRC front end with more of the features you get in real IRC clients.
It is also themeable so can be made to look seamless with the site design.
(you can test the demo site with any freenode room)