Hmmmm... while this is not directly connected with the problem discussed... I did have a weird problem once with my KVM switch. (I don't have any Amiga hardware connected with my KVM switch, though....)
I had switched to a new dirt-cheap multimedia keyboard from Big Lots... which worked for awhile after the systems were powered on... but then after a few hours, in Windoze XP the mouse started behaving oddly, and so did the keyboard. The scrollwheel on the mouse started causing the browser to behave as if I'd hit the back-button and front-bottom instead... steadily scrolling backward and forward between pages instead of scrolling the page up and down like it was supposed to. And the keyboard switched to all caps on its own, or something of the sort, and I couldn't get it back out, and the KVM stopped responding to the ScrollLock key.
If I powered all the systems off and powered them back on... and then left it a few hours, things went back to misbehaving again as described above.
When I powered everything off and switched back to the previous keyboard, all the problems went away. And when I later switched to a different multimedia keyboard, it also worked fine.
I'm guessing that the cheap keyboard took slightly more juice than was expected, and was drawing down the available power coming through the KVM switch meant for the keyboard and mouse... so that both devices started misbehaving after a few hours.
At that, it might have been a faulty keyboard (I haven't tried it on a KVM-less machine yet...)
Just something to bear in mind...!