When is used used up?

Norman - Not likely to find White Papers on basic stuff like that.

Amp's output current flows from power supply capacitor thru it's Equivalent Series Resistance (ESR) and Equivalent Series Inductance (ESL) then thru output transistors and speaker to come back to power supply capacitor.

Amplifier attempts to regulate/mantain required voltage level but power supply cap's ESL will make it less than perfect at higher frequencies while it's ESR if high enough will cause high voltage drops and eventually amp will run short of voltage.

ESR of capacitor is constantly increasing because of drying effect up to point that after long time self heating (big current x ESR) will cause thermal runaway effect (ESR increases with temperature) and capacitor might even explode. To prevent catastrophic explosion all larger electrolytic caps have built-in fuse (rubber plug).

Quality of sound depends on quality of power supply caps (ESL, ESR, leakage etc). Best caps have extremely low ESR and ESL. Sometimes people bypass electrolytic caps with much lower inductance film caps (to speed-up response) but this creates parallel resonance circuit with ESL (and therefore ringing).

Kijanki is correct - the operating parameters of electrolytic caps are constantly degrading primarily from heat. While the actual capacitance figure in microfarads may remain fairly stable, ESR, dielectric absorption and leakage current are constantly degrading from use. Unfortunately, without something like a Sencore capacitance analyzer, these parameters are difficult to check. Electrolytic caps with any type of case deformation (bulges, etc), or white residue around the rubber gasket at the base is overdue for replacement.

Depends on the gear.
I have a 1961 Bell tubed integrated amplifier with the original RCA 6v6 and Telefunken tubes.

I have owned it for almost 5 years, and don't play it much, but I've never had a problem.
As far as how many owners and how much use it has had I am not aware of, only that all the insides are stock, and no mods.

Everytime I take it out and insert it into my main system, it works,perhaps I am just lucky and it's on borrowed time.

The strange thing is, this unit isn't too far off the mark from some of my more expensive gear and certainly not tubey sounding or rolled off and distorted like some of the 1970's solid state receivers I have heard.

That being said,I just don't understand how gear from the 1970's that was mid fi, mediocre, seems to have taken on cult status and is referred to as Vintage and demands big bucks.

To me it's just old, it wasn't great then, how could time have improved it?
So to me if it works, you like it, got it for peanuts, then congrats, but when it needs fixin, it's useful time is up.

When repair costs exceed market value?
When repair costs exceed nostalgia value?
When you decide to replace?