Thanks for your bug report. I have not been able to reproduce this issue so far, however if you can provide some more information about when this issue happens, I may be able to track it down.
If you install a clean copy of mIRC in portable mode to an empty folder, copy the OpenSSL DLLs into that folder, and then run mIRC from that folder with default settings, do you still see the same issue? Do you see the same issue with both OpenSSL 0.9.8y and 1.0.1e? When does the issue occur? Does it happen the moment you run mIRC? Immediately after you connect to a server? Or later on?
Also, are you using anti-virus software? Sometimes if an anti-virus software signature database has not been updated to recognize the latest version of mIRC, it might think it is not authentic and will block it in ways that might cause side-effects like this. If you disable your anti-virus software, does that resolve the issue?