The one thing that tends to "wear out" with solid-state amps is the capacitors ("caps"). In a decent amp, they tend to last many thousands of hours, therefore providing years of use, but they do fail over time.
Provided that an amp does not run really hot, like a pure Class-A design (e.g., Plinius, Gryphon, and certain Pass amps), the best way to increase longevity is to keep it powered up 24/7. The thermal cycles that a component experiences when it is turned on, whereby it heats up, and then turned off, whereby it cools down, is harmful to the internal componentry, making parts brittle over time and inducing failure. 24/7 operation does wear out caps faster, but caps are relatively easy and cheap to replace - they can be viewed like tires on a car (albeit a set of tires that gives you 300,000+ miles - caps last many years). What you don't want to have happen is output transistor failure, because they have to be matched and occasionally even go out of production - this is the most compelling reason to keep the amp on 24/7.
That said, you do not want to keep a pure Class-A biased amp, or other designs that run really hot, turned on 24/7, because high heat also degrades parts and thus can induce failure (not to mention the large amounts of electricity that Class A-biased amps consume).
Likewise, it's arguably okay to turn on and off a cool-running Class D amp, as such amps really don't experience thermal swings when turned on and off - they're always cool.
To specifically answer your question, a decent quality solid-state amp that has not been turned on and off with each listening session, and that has its caps replaced every ten or twenty years, should never fail. Of course, this assumes that the owner takes necessary precautions in the event of weather events and other hazards - equipment must be unplugged from the wall in the event of electrical storms (lightening strikes can destroy audio equipment), moved to high ground if there is a flood, protected from children, pets, house cleaners, and drunks, etc.
