I have a similar issue via a 5-way switch;
I loose the connection if I reboot the NUC, and the NUC isn't selected on the hdmi-switch.
However I am able to switch between devices... until I reboot.
From a thread I read on the forums earlier, I believe an Intel rep suggested using an "active" switch. What I'm using now is a "passive" switch. From what I understand, the "active" switch would keep the HDMI communication open with the NUC, and not become upset by loosing attention.