Well, I don't know the settings for your router, so I can't be much more help than to explain what happened with mine (until I set the internal IP to static)...
My normal internal IP was 192.168.1.1 and another computer on the network was 192.168.1.2. The router will reissue the license to the IP addresses every so often and would sometimes swap me to be .1.2 instead of .1.1. Because all ports were set to .1.1, my computer no longer had those ports forwarded to it. By setting my computer as static in the router (not static from your ISP), I didn't have to worry about that again.
Another option you have is just to turn off your router and modem. Wait 15 seconds or so and turn on your modem. Let that start up completely (all solid green lights, with the exception of the PC Activity light that usually flashes amber). Once it's fully started (about 15 seconds), turn on your router and let it start up completely. Then try mIRC again and see what happens. Sometimes, that's all that is needed.
You may also want to check your Localhost info in mIRC's options and make sure it matches with what it should be.
