You will need to have your router and/or firewall set up with the same ports as you have mIRC set up with. mIRC defaults to ports 1024-5000, which is considerably more than are necessary. Usually, you can set that to around a range of 20 ports and be fine (1024-1050, or 5000-5020, or whatever you want as long as those ports aren't used by some other program you run such as games or P2P software or any other internet software). To learn how to set up the ports with what you have, visit
http://www.portforward.com/ . There, you can choose the router you have and choose mIRC and you'll find out how to set the ports up correctly. Also, it's usually helpful to set mIRC's port options to randomize ports.
Beyond that, if you have the same ports set up in both mIRC and your router/firewall and you still have problems, then you might first want to pay attention to the ports you are sending files on. See if the failures are all on the same port. If so, then you might have a program that uses that port. In that case, choose a different port range.
You also have the option of using DMZ on your router, but that basically opens all ports and isn't a good option for long-term use.
And there's the option of Passive or Reverse DCC. Newer versions of mIRC have a Passive option, or you can use Invision's Reverse DCC option. These both work basically the same. It reverses who initiates the connection. Routers and firewalls rarely block outgoing connections and only block incoming connections because the incoming connections are usually the only ones that you really want to block. So by reversing the connections, it means that you don't have to set up your router/firewall correctly to achieve the connections. The problem with this method is that the person downloading has to set the ports up themselves instead of you. If they are in a situation where they cannot set up their router/firewall ports, then they won't be able to download from you. So it's a final option when you can't send normally. It works, but is limited to only those who can set up their ports.
Some things to also consider... You may have Passive or Reverse DCC already enabled and those who cannot download are those who can't change their ports. The fix for that is to turn those options off. Or, the people who cannot download are blocking the downloads. They may have specific filetypes blocked (such as RAR, which is blocked by default) or they may have DCCs blocked completely.
You can find me at #Invision on irc.irchighway.net or #OldGames on irc.undernet.org if you need me for anything.