Can the sound of SS amp deteriorate over time??

Bdgregory and Soulbrass are correct. Electrolytic Capacitors do dry out eventually, reducing their effectivness. I would imagine decrease in sound quality would be the first to go, followed by eventual failure. Electrolytics have a conducting liquid inside, sort of like a so-called 'dry' cell battery, but the capacitor liquid is less viscous than a battery.

The sound of all gear will deteriorate over enough time...

....and so does your hearing.

Yes, electrical products can and do shift operating parameters over an extended period of time, especially if tempurature swings are involved. Sometimes, a simple alignment is all that is needed, sometimes parts need to be replaced and then an alignment will solve the problems. It all depends on the original design, how well that design was implimented, the environment of the gear ( in terms of ventilation and exposure to dust / airborne debris ) and the operating patterns that it has to deal with.

I get some units that come into work after 30 years that work and look like new. I get some other units that are two years old and look / work like they should be put out of their misery. As such, even a poor design can last a long time if it is babied and a robust unit can be falling apart if thoroughly abused. Most units are somewhere in the middle and therefore don't need a lot in order to bring them back into spec. That's why companies like Bryston can give the warranties that they do. Sean
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Short of bench testing an amp to determine if it meets spec, there is no way to tell for sure. Many, who consider measurements verboten, foolishly waste time & $ with ZERO improvement.