[Link: bkcomp.com], page 4.

"Amplifier pairs with DIP switch ‘SENSE’ set to ‘ON’, have the remote Master and Channel switching of
the amplifier audio mute on/off feature disabled. Amplifier pairs set to use ‘SENSE’ will mute
automatically after a delay of three minutes once no audio signal has been detected. The sense circuit
monitors the amplifiers selected audio, i.e.. ‘Local’ or ‘BUS’ mono or stereo. When remote amplifier audio muting
is desired by either the Master or ‘Local’ Channel control input, the ‘SENSE’ switch must be set to the ‘Off’
position. When the AMP ON feature is desired or automatic muting of the amplifier pairs is not desired, or if the
audio signal is erratic, the ‘SENSE’ switch must be set to the “Off’ position.
1 2 3 4
ON"

Not the best use of the King's english, but it _is_ right there.

As far as the ST-55.2 getting powered off, how about a triggered AC gizmo like the Niles AC-3 or just plugging the amp into the switched outlet on the receiver, considering that they will likely reside in the same cabinet.