For Krell owners, keeping the amp on all the time?

Many amps (pre's & cdp's/ dac's) works like this, they just mute the output stages and dim the display. JRDG, Wadia (CDP) aso aso.., why don't you just check what the manual says about idle power consumption if you are worried? That piece you have is pretty small if compaired.

I would assume "standby" and off are two different things. Seems to me that standby would probably be a prudent compromise.

The problem with "Standby" in most amps is that it turns off the output stage, i.e., the output transistors are turned off, thereby going cold and contracting in size, and are turned on when taken out of Standby, thereby heating up and expanding in size. Thus, if Standby makes your amp go cold, your amp is experiencing thermal cycles when the amp goes in and out of Standby, and generally speaking, this will increase the likelihood of catastrophic amp failure (e.g., loss of output transistors). In addition, a cold amp will make your system sound mediocre, particularly if you have a high resolution system.

Some amplifiers use the standby as a bias changer, during standby the amp is in Class AB and when on is in Class A.

Sometimes I don't listen to music for days (let's say 3-4 days), so is there any worth of leaving the KAV 300i on all the time?