I can't reproduce this
//write test.txt hi | dcc send $me test.txt | dcc send $me test.txt | dcc send $me test.txt
Works fine for me
However, one reason it could fail to work is because of flood protection settings.. some scripts, or even some mirc settings (like Alt-o -> DCC -> Ignore) can ignore sends for 3 minutes.. I assume this might be the issue and would explain why you would send the same file more than once (because the first one was ignored).
Other than that, I don't see why you'd need to send the same file to the same person more than once in a minute... It certainly makes sense to me why mIRC would intentionally block this behaviour by default.