Just picked up a ROC-SA headphone amp used and it runs quite hot. You can put your hand on it and leave it there but its right at the point of being too hot. Is it safe to leave it on 24/7? Might it fail prematurely if I do leave it on?
Why would you want to leave it on? Besides the heat shows how inefficient it is which means its consuming a lot of power. There's no nead to turn it on and off 20 times a day but I would not leave it on.
If you want some encouragement, pull up datasheets for capacitors over at Digikey or Mouser. You'll notice a stat called MTBF, or mean time before failure. It will be listed in hours. That's the amount of time before a component is expected to fail. 2,000-3,000 hours is pretty common.
By failure, I don't mean a Hollywood-style explosion or anything. That can happen, but probably won't. Failure is usually defined as a part that goes out of spec. A .01 cap might turn into a .1 cap. That will change the sound and potentially damage other components. At the very least, it will alter the sound and need to be replaced. It's hard to tell by ear, as well, because the value change will be gradual.
Heat is the destroyer of electronic components. The more heat, the shorter their lifespan. Further, everything was designed to be turned off so it can cool down. Only specifically made industrial parts are designed for 24/7 use, and you won't find those in audio gear unless you DIY with them.
As for the general creep of deterioration, I conducted an experiment with that once. I was wrenching on an old tube radio and replaced its filter caps. It worked well enough with those replaced. But the old wax/paper caps inevitably die and carbon comp resistors are always out of spec. They all had to go. Instead of going straight through, I decided to turn it on after each component was replaced. Took a little longer, but there was a steady improvement after each out-of-spec part got a new replacement. At the end, I gave it an alignment and fired it up.
I hate the phrase, but there really was a night and day difference. It worked with the nasty old parts, but sounded amazing when the circuit was brought back to correct values.
So don't leave you gear on all the time. It will deteriorate.