Thanks for the bug report, I can't seem to reproduce the issue here yet. I tested with mIRC 6.21 under Vista with all Agent speech enabled, and then connected to several servers, joined channels, opened dcc sends/chats and it all seemed to work fine.
Are you able to reproduce this issue every time? Or was it a one time situation? Does it only happen with dcc chats? If you install a clean copy of mIRC in an empty folder, with no scripts etc., and test it out, does the same issue still occur?
