The question not yet asked: How often do you use the gear in question?
If you are listening every day, if others might use it during the times you are away from home, if you listen almost all day on weekends, then you might consider leaving the AVR powered up continuously.
If more than 24 hours transpires before you are listening again, definitely power it down. What about if you use the components often, then? That's where it becomes a little less clear.
Surges in the power supply (inrush current) and temperature changes definitely have a wear factor that is part of the determination of component life. The difficulty is knowing exactly "how much" this is an issue, and the unfortunate answer is "it depends". Some gear tolerates startup better than others, some gear tolerates long power-up time better than others. Some gear happily tolerates either or both.
You are unlikely to know which is which from a perusal of the spec sheet; you probably would, at a minimum, need to pop the hood and look around inside, checking capacitors (and downloading the manufacturer's literature to determine the specifications), assessing layout, maybe even measuring temperature of the heat sinks when in operation (don't do this if you don't know what you are doing, or use a laser temperature probe which doesn't require contact).
As the manufacturing budget gets tighter, these are the areas that are compromised to drop the retail price, and these are the areas that are likely to give problems with operating heat and turn-on surges. Some manufacturers estimate how often their components will be used and for how long, and cut costs accordingly. In other words they are deliberately built *not* to be left on continuously.
It's one of those intangibles that premium components should offer that might not reveal themselves from the spec sheet. And the exact answer will change with every specific model, including units by the same manufacturer higher or lower in the catalog. So, there is no "one size fits all" answer.
Well, maybe there is one. If your gear is not properly ventilated, with adequate space around and above the components, you definitely should be powering down, even for brief interludes. You already are stressing everything and are already on the way to short component life.
