I had the Korato class A amp here for a while and I can say that it needed at least 6 hours to open up, but still sounded better after a full day (24 hrs). This is one amp that needs to be on all the time, and being class A, it throws off a bit of heat and uses up some energy, even at idle. I've heard this about class A amps, so I think the answer there is a definite "yes, on all the time".
My regular components however need about 20-30 minutes to warm up, but I do think they sound better yet after an hour or so. That is definitely true for the tubed components (preamp, phono stage). On all the time? I think not, but definitely better with some time turned on.
Enjoy,
Bob