That KVM gets power from the USB port.
Desktop PCs tend to send more power to the USB ports than Laptops.
Things to try:
a) fiddle with the power settings on the laptop to make sure that the USB ports are powered on all the time, and not powered-off to save battery.
b) try a different USB port on the laptop
c) sometimes you have to fiddle with the USB settings in the BIOS of the PC or laptop to enable what's called 'legacy USB support'. Legacy USB support helps the KVM to wake-up, and makes sure that the keyboard works in DOS and in the BIOS setup screen.
d) Some USB KVMs are just flaky, and doing things like having one PC go into sleep mode will totally hose the KVM.
e) Some KVMs do not support using using a wireless keyboard/mouse, if that's what you' re doing.