AFAIK, this is not possible, as the handles to Wine's (or any other X client's) windows evaporate with the X server.
About the best solution would be to run a non-GUI backend, such as ZNC, and connect to that with mIRC.
Alternately find some other way to accomplish what you're killing X for. It's possible to do a lot of weird wrangling of your desktop environment (like changing window managers) without restarting X. (But this is beyond the scope of this forum.)