I have worked with tube equipment for years, so I will toss in an opinion here. In general, you want them off, since they don't age in the off condition. When they are on, you are burning the cathode coating, which is the fundamental part of the design. In addition, a max'd out plate supply will also wear the cathode coating likewise for max'ing the current flow through it. Running tubes at reduced power plate supply and current increases the tube life exponentially. Those are design issues, so once the designer has made all the tradeoffs, the tube life is set for the amount of run time it is on. The best you can do is turn it off when not using it.
Now, that being said, a lot of turn on and turn offs don't help things either. So if you are listening, then leaving for a hour or less, and plan on listening when you return, I'd say leave it on rather than do a power down and a power up. If you are gone for 2 to 4 hours, then a power down and power up starts to make sense. Certainly, if you are gone for 4 to 6 hours or more, you will probably want it off.
Remember, tubes burn power, which runs your grid meter, which makes your power company profitable. Spinning that grid meter when no one is listening uses money that really could be saved to buy new tubes.
So in general, avoid a lot of power ups and downs in a short time, but don't burn power when no one is listening. There is no magic rule here but that is a good general one.
Now, that being said, a lot of turn on and turn offs don't help things either. So if you are listening, then leaving for a hour or less, and plan on listening when you return, I'd say leave it on rather than do a power down and a power up. If you are gone for 2 to 4 hours, then a power down and power up starts to make sense. Certainly, if you are gone for 4 to 6 hours or more, you will probably want it off.
Remember, tubes burn power, which runs your grid meter, which makes your power company profitable. Spinning that grid meter when no one is listening uses money that really could be saved to buy new tubes.
So in general, avoid a lot of power ups and downs in a short time, but don't burn power when no one is listening. There is no magic rule here but that is a good general one.