it appears that what is most likely a relay is connected directly between the signal pin and the ground sleeve of the RCA input connector on each channel. Presumably when the warmup period concludes a control voltage is applied to the relay which causes its contacts to open up, allowing the input signal to proceed to the input stage. And presumably when the amp is turned off that control voltage goes away and the contacts close, resulting in a short across the input.A modification may solve the problem:
INPUT NO
@-------------o
| \ R2
| O--------WWW------
| C
|---------------o
| NC
|
V
GND