It seems KVMs never work just right.
It is my experience even the more costly ones are just cheaply made. They use cheap cables, cheap and poorly constructed cable connectors. And poor quality components inside the switch. The pure "intelligent" switches (no moving parts) are better, but not immune to premature failure.
If you swap the connectors to the other computer, does the problem move with the cable or stay with the same computer?
Make sure all the cable connections are tightly fastened. If the switch is mechanical, you might be able to open the case to expose the contacts then clean them with some quality
electrical contact cleaner.
BTW, that miniture DIN connector is called a PS/2 connector.