Is age bad for solid state amps?

yes the caps leak and get hard

its possible to be in fine shape.

Any local tech should be able to recap the amp for you, if you are at all adventurous you could do it yourself as well. As Jaybo said it is possible it will be in fine shape, it could possible go many more years.

at least one manufacturer recommends replacing capacitors every 10 years or so. Many mfg's though say don't bother til they break. Most other parts are good for nearly ever I believe, except maybe panel lamps, or electro-mechanical components such as switches.

yes yes and yes..caps go bad transitors die a slow death and all other parts including boards have there own life cycle.Just like us.