Monitor not waking up after switching KVM input
While I do not have an answer to your problem, I can add a "me too" with having issues with KVM's and El Capitan. I have an ATEN CS1944 kvm that works just fine with everything up to and including Yosemite. When I convert machines to El Capitan the the KVM and the machines freak out when the kvm shifts focus away from the El Capitan machine and then ultimately requires a reboot of the affected machine to get things going again.

Tried numerous work arounds and tweaks with no success. Between this kvm issue and the other issues that arose with the converted machines not playing well as XSAN clients (kept randomly failing to auto-mount the xsan volumes) upon machine startup, I had to bite the bullet and fall back to Yosemite on the 2 converted machines that were attached to the KVM.

I guess it will be a wait for KVM firmware updates and or OS X patches / fixes to try again after the product matures a little more. Keeping the fingers crossed and continuing research for a fix.

Good luck with resolution to your issue as well.