I don't believe the problem has anything to do with scheduling (allocating time-slices to the CPU) as others have suggested. As you've mentioned, if other programs have the same priority as mIRC and are requesting CPU time then they will have more or less equal allocation as mIRC.
I think the issue in your original case is that you are constantly accessing the clipboard from mIRC while the clip.exe process is trying to write to it. The clipboard is essentially a global resource so if mIRC is accessing it clip.exe has to wait until mIRC releases it again.
Note that this is just an assumption on my part, I haven't tested to confirm this.
