I have this issue with my LC III under System 7.6.1. If you leave it in that state long enough, the mouse pointer will freeze also. It has never bothered me enough to try to figure it out, but I believe it to be something wrong with my System installation. If I boot from a floppy it doesn’t happen. A clean install of the System would probably fix it. Since it seems to perform the normal shutdown process before freezing though (I never get the “It appears you didn’t shut down your computer correctly” dialog next time I use it), for me fixing it would be more trouble than it’s worth.
Long story short, try booting from a Disk Tools floppy for 8.1. If it doesn’t happen when you boot from the floppy and it really bothers you, peform a clean install of 8.1.