Sounds like either Windows or mIRC doesn't like having that many windows open at one time, which is kind of understandable (from the mIRC point of view), since mIRC is, technically, supposed to be used for chatting, and I don't know anyone that could keep up with 200 chat rooms, not to mention the fact that each chat window would be so small, if tiled, that you probably wouldn't be able to see the text anyways.
As to getting around it, the only thing that I can think of as a possibility, is to have multiple instances of mIRC running.
An example might be, 5 occurances of mIRC connected to 4 networks each, and 10 channels per network. Mathematically, that gives you 200 channels, yet each occurance of mIRC only has 44 windows (40 for the channels + 4 for each status window for the connections)
You might also think about hiding the windows that are realistically irrelevant, such as the status windows, using
/scon -at1 window -h "status window"
That will hide the status windows for all of the connections that that occurance of mIRC is currently connected to.