Facing the same issue. I also think it's related to the latest kernel / firmware somehow. Not sure if it is a Displaylink problem at all, maybe it's connected to USB firmware.
I have only bluetooth mouse / keyboard and cannot connect my monitor directly to the laptop. Maybe to test, can you connect everything directly to your computer and see if keyboard / mouse stop working at some point? That would indicate a problem with the USB firmware itself which then kills our displaylink docks as well