Headphone amps are quite similar to guitar amps and the components do wear out.
Pull up a datasheet on a capacitor at Mouser or Digikey. You'll find the mean time before failure (MTBF) listed in terms of hours. Nothing lasts forever.
Failure does not mean it won't turn on or go up in flames. It usually means that the part goes out of spec and that it no longer operates at the value specified in the circuit. This is tricky to hear because the parts slowly change value over time. But if you recap an old set (and preferably get the old resistors out, too, since they drift) it'll sound different when plugged back in.
The only parts that keep their value over time are wirewound resistors, transformers,mica caps, and the air gap capacitors used for tuning radios. Everything else degrades.
This is also why I'm a fan of point-to-point construction for tube gear. If you need to replace parts on a PCB, you have to unsolder the jacks, switch, power supply, and other stuff to get the board out. Once out, it's easy to lift pads, damage traces, and have other problems with the PCB. Those can be tough to fix. Further, replacement parts don't always match up with the PCB holes and sometimes space is an issue.
Point-to-point will let you get a bad part out and replaced in a few minutes, no disassembly. If a wire is damaged, a new one goes in just as fast. If you want to put in bigger parts, no problem. It costs more to build that way, but it will hold up forever and can always be repaired.
