I guess esspey's problem is NAT related...
With prior mIRC versions, I had no problem with DCCs & DCC Resuming. (btw, I'm using a NAT).
In mIRC 6+, in some case (seems to happen when both you and the remote user are using a NAT), mIRC won't resume files and shows "* DCC RESUME rejected: incorrect parameters" or some similar message...
As I stated before, I had no such trouble before (when running mIRC 5.**), this all started when I updated to mIRC 6+, and only mIRC changed in the while, my NAT & Windows' settings remained the same...