Keep on power surge protector all the time even when system off?

Agree with @dweller . If your gear is plugged in leave the surge protector on.
 

Thanks,  I have a McIntosh MPC500 and spoke with them.  Even if the display is off by pressing the Outlet button, it is still functionally ON and protecting the system according to them.  The LED lights below each numbered outlet remains lit at low level.  I was concerned as when I powered off my Mc pre and amp to standby, the MPC500 display also shut off. 

If your equipment is plugged into electricity, you should protect it from surges e.g., a lightning strike or when power company restores electricity after a power outage (turnes power back on). If all of your equipment is unplugged, you obviously don’t need the surge suppressor. Furthermore, some surge suppressors are actually designed to burn themselves out to save your equipment (sacrificial) and must be serviced or replaced when this happens.
So it's a good idea to unplug everything if you're not there for an extended period. Hope this helps.