Hi there,
I'm also a Nad fan. I find this pretty odd that you should loose two in such a short space of time. The cutting out is due to the "protection circuit". I would be inclined to get your speakers checked out as if they are faulty or not "matched" to the amp, it will trigger the amp to "protect itself" and shut off.
My solution was actually indeed the output protection relay. What I did was to open up the relay and use contact cleaner and a very fine abrasive to clean the contact surfaces of the relay. After that, the problem was gone!
The way to diagnose this for me was to run the amplifier open until the problem recurred and to simply tap the relay's box. The sound came on immediately, and I was convinced.
The hum of course is the 60 cycle line AC voltage. Make sure that the routing of the AC power plug is as distant as possible from the stereo RCA cables.
The most likely problem is the connection of the phono cartridge to the wires in the arm. These connections usually are silver plated and become oxidized creating a bad connection. Remove the cartridge and using a fine eraser polish the connections. There is a ground connection that makes the five wire connection. Be super carfull these terminals are very easy to break
The phono connections to the stereo is very low voltage subject to interference. The connection to the magnetic pickup at the tone arm is low impedance and is inductive. Any poor connection between the cartridge up to the AV316 will produce this hum. Continue to check connections and swap cables with a known good to resolve.
I have switched the left and right cables to ensure that the cable is not the problem.
Hope this helps?