As noted above, the primary source of heat in class A SS amps are the output transistors. That's why they're mounted on the heat sinks. However, if they are used properly and have adequate temperature control, they're probably not going to be the first things requiring maintenance.
Capacitors, in particular the ones in the power supply, will age the most rapidly. While their eventual failure could prove catastrophic, long before then they will suffer from lost capacitance and increased ESR, which means less power available and more noise. This is why Nelson Pass, whose primary interest is sound quality, gives different advice than a person that is just looking to get the most use for their initial outlay.