That is indeed odd. Full system specs would help us figure out what's going on. I can tell you right now it isn't the graphics card or the processor, but otherwise it's difficult to say. It may be OS related, or a problem with the mouse; you may look for patches/new drivers on those. Also, have you tried unplugging every USB device except the keyboard (if applicable) and mouse? I've heard of some strange conflicts that can occur with USB devices and they are really difficult to spot.
EDIT: and does the mouse fail completely before or after the start of a mission (i.e. still work in the main hall but stop working in game)? And do keyboard commands work when the mouse is frozen? Just more details that would be most helpful in finding the bug.