Should a CDP be left on 24/7 or shut off & on?

Isn't that a thought?

I leave all my gear on fulltime and turn the dac and cd transport's display's off.

The Capitole is on all the time unless you turn off the switch in the back. I have a friend who has been concerned with lightning strikes, so he turns off his DarTZeel and Capitole II. It's awful. I ask him to put the system on in the morning if I'm coming over at night.

It simply doesn't fill out without being on.

Those players with a tube front end benefit from being on 24/7. But if your not going to play for extented times then it's a good idea to turn them off. This will prolong the life of the tubes. I haven't heard of anyone leaving units with out a tubed front end on 24/7.....

I turn my system off (always have) when not using it. I believe it stabalizes in 10 or 15 minutes. I don't hear any difference and figure I'm saving precious resources.
Also, I've come to the conclusion that I don't listen with the same intent or intensity as some others on this site.

If it doesn't have tubes in the output, leave it on all the time.

No harm in leaving it on. Having said that...if the player has a standby mode you can probably use that. Most better players with standby are designed to leave that part of the player on that has the long warmup parts; and they shut off things like the display and the transport which don't matter to save power.

My CDP specifically says this in the manual.

Check the manual or the manufacturer if you like. Cheap players also have standby, but they really only leave enough on so the remote can turn it back on.