We’ll probably need some more information to help debug. I’m not super familiar with the twitch-irc node.js package, but a place to start in order to narrow it down:
Are you able to telnet to the twitch IRC server from outside of your application?
>telnet irc.twitch.tv 6667 Tue May 26 19:49:20 UTC 2015
Trying 192.16.64.152...
Connected to irc.twitch.tv.
Escape character is '^]'.
NICK test
:tmi.twitch.tv NOTICE * :Error logging in