Most SS amps fail at turn-on when they fail. If they have a soft start circuit not so much. Solid state devices don't age like incandescent light bulbs, they really don't know how old they are, especially if they are operated inside their thermally safe margins so as to avoid derating.
If the amp is left on 24/7 it is more likely to be subjected to brown-outs and AC switching transients during power outages, these dangers also have to be figured into any potential advantages derived from being left on. Power strips and power conditioners with MOV surge protection are a good thing to have in place.
I have run my SS amps and my front end gear, 24/7 since the late 90s and have encountered no problems thus far. My reasons for 24/7 operation have to do with warmup time and storage capacitor behavior. The amps have sounded noticeably better when they have not been turned off. That being said, I do not have Class A power amplifiers, if I did I might be turning them off to avoid the heat and power bills that would be associated with 24/7 operation.
If you can't hear any sonic benefit from leaving the amp on 24/7 then you should probably turn it off when not in use.
Scotty