I believe I said earlier that the problem had been resolved when I disabled XP's firewall. Over the last few days, I found this is not entirely true. I had been using mIRC 6.03 to connect to EFnet, which no longer seems to have the problem, but 5.9 to connect to DALnet. After switching to 6.03 for both, I found that the problem still happens on DALnet.
Again I want to stress that it does not happen when using mIRC 5.x, only with 6.x, so please don't respond saying "DALnet is having problems." I know that, and if this were related to it it would happen regardless of which version I use.
I don't expect an answer this time. I just wanted to everyone know that disabling the XP firewall did not fix it for me. It seems that everyone who has this error finds a different problem and thus a different solution. I will thus be looking into my specific problem further when I find time. Thanks for the help.