That's a tough question to answer because it depends on both the product design and the environment it's operating in. Here's my general list of electronic killers.

1. Operation in high temp / high humidity environments. Moderate heat isn't really a concern. Once the humidity gets above 90% I start to worry about my electronics. The hotter it gets, the more I worry. Under extreme conditions the electronics can suffer from a problem called solder migration which causes shorts.

2. Voltage and current transients. These happen anywhere you have inductive and capacitive elements and you make or break power. You'll get these when you turn on your amp AND when you turn it off. These can cause elctrical overstress which causes components to fail.

3. Thermal Shock. Rapid changes from cold to hot or hot to cold can crack solder joints or cause smaller components to crack (surface mount caps have always given me fits).

Leaving your equipment on you run into the life shortening effects of heat and humidity (#1). Power cycling you run into into the life shortening effects of #2 and #3. Good design can mitigate some of these effects but I can't in general say which would be better. Whoever did the validation testing on the electronics can give you a better idea of where the weaknesses are but they tend to be pretty tight lipped individuals.

Unlike me who uses many words to say I don't know