You could enable port forwarding or triggering for your mIRC DCC ports. You can specify DCC ports by going to mIRC Options > DCC > Options in the DCC Ports box on the right.
I've got the same problem and I use a Microsoft Wireless Router. Got any ideas? I don't understand the forwarding thing and I can't find it in the help file.
If port forwarding isnt in the manual that came with your router, check their website...they may have more how-to info or try one of the general links in the thread Poppy suggested.