I have seen this problem before, its a peice of hardware maybe your router adjusts the port range of incoming files, you must understand that when you recive a file, you actually recive first a message in mirc like this "DCC SEND filename IP port size", you then make the connection to the person who is sending you the file, this method is used to bypass your firewall, as you make an outgoing connection.
heres the likely problem. the sender of the file sends this message in mirc as follows. "DCC SEND blah.rar 3389006414 5000 200000000"
3389006414 is the senders ip
5000 is the port
200000000 is the size
your hardware doesnt let you have that port so alters the port number to one it lets you have say 23000, all goes well becuase when you connect out using 23000, it adjusts this to 5000 for the sender, the problem comes if you go to resume, when you do this you send a resume request as follows "DCC RESUME blah.rar port size" aka "DCC RESUME blah.rar 23000 150000000"
23000 being the port you were told to use
150000000 being the size of the file you have
now when the sender gets this, his mirc or what ever hes using just goes to itself , "Im not sending anyone a file on port 23000 so im going to ignore that message" and thus your resume request is declined, and you get a timeout situation.