From a lifespan viewpoint, any heat is bad. Thermal cyclic failure is logrithmically dependant on power (half the power = 100 times more cycles before failure) so especially high power amps should not be turned on and off too often. But, if it is on all the time, the cycling effect is decreased because when you turn the volume up from idle, the device temp is not starting from room temp which increases your device lifespan compared to cold starts. The happy median point is very hard to find due to its dependancy on many factors like circuit design, layout, device type, bias, heatsink, size, weight, etc.
That said, some designs (like emitter-follower and low or zero feedback) can have thermal issues after being on for a long time like bias error which will degrade performance over time especially if extreme care in hotspot minimization was not taken. I would ask the manufacturer as to what to do (although they may be reluctant to tell you that they did not design for full thermal steady-state). If everything was taken into account in the amp design - there should be no problem in leaving it on all the time, save higher electric bill.
But as for me, I stay away from class A due to thermal problems (as I said - any heat is a problem) and because designers who like the concept of "pure" class A often tend to oversimplify the circuit to the extent that it cannot take care of itself in the long run or in extreme situations. I am always amazed how many high-priced amps have little to no protection circuits in the name of clean and pure sound, which I think is a very dumb idea. Arthur
