Well, I've never heard of it doing it 3 times in a row... the 2-time ad when joining is an issue we know about.
Although I've not tried, I am told you can turn off autostart. Then, just don't stop your fserv when you quit. It should stay active and if it's not on autostart, it will only display once.
You can also do an edit to the timers. This is available in this .
Finally, if you set a delay when connecting before joining channels to something like 10-15 seconds, it won't display both times. And, again, I don't know about that third time.
Never connect to the same network more than once with Invision or you risk losing your settings. If you want to connect multiple times to the same network, use two copies of mIRC... one for serving and one for chatting (or whatever). mIRC takes few resources... just run two and have at least one of them minimized to the system tray so it's out of the way.