I'm going to go out on a limb and say that Khaled's response still makes sense. Both mIRC clients have an open identd port, usually port 113. Therefore, both clients will attempt to accept any connections on the open 113 port they are listening for. I tried to reproduce this, but it does not happen on my end (v7.32, Win7-64bit).
If you are connecting to multiple servers via #1, and #2 is idling, doing nothing, then perhaps it's the strain you are putting on #1 that is allowing #2 to act quicker and take precedence when replying to the identd requests from #1.
