When the PC wakes from sleep it'll rescan the monitors, because you might have unplugged something while it was sleeping. It looks like the KVM keeps telling the PC there is a monitor connected even when you switch away from that input (as it should, to avoid unnecessary window rearrangement) while the PC is running, but when the PC awakens it does a full rescan and decides it can't make sense of what's attached and so falls back to classic VGA.
Sounds like a similar problem.
You might also be able to force the PC to output a specific resolution irrespective of what the monitor/KVM says. It's a bit like installing a Monitor Definition File on your Acorn. I've done that on Macs and Linux but I'm not familiar with how Windows does it. There's probably an app for that.
Theo