It's just chemistry.
The reaction that makes electrolytic capacitor insulation is one of forcing oxidation of the base metal driven by an electrical force. This makes the reaction proceed faster, and to a greater depth than is possible by the simple reaction of oxygen in the air with the base metal. It may also force a slightly different oxide or crystal format that open air oxidation. I don't remember THAT much chemistry.
A lot of this is in the Tube Amp FAQ at GEO, by the way.
The electrical force is combatted by the growing oxide thickness. If X thousandths of oxide thickness grows in just air, then X +Y thousandths grows by electrical forcing. Since the oxide is an insulator, the growth insulates itself as it gets thicker, and V volts grows Y thickness and then stops. If V is a bigger voltage, it causes a bigger Y thickness and stops there. Any voltage up to about 500V or 600V is possible; it gets impractical or impossible to grow aluminum oxides thicker than that.
The oxides grown on the foil of electro caps is a bit of an unnatural one, otherwise it would grow in air. So all by itself, it UN-grows with time, relaxing back to the more natural state. How long this takes depends on the conditions the oxide is in. If it were kept in liquid nitrogen, it might last for a very long time. Keep at room temperature in a semi-wet electrolyte, it un-ravels enough to make the manufacturers not want to warranty caps after about 5-10 years of shelf life. That means they think that there's a fair chance that the cap will no longer hold its rated voltage if it's suddenly applied after that time.
In a circuit, the voltage across the cap is in the correct direction to re-form the oxide. So there are competing effects between aging and heating UN-making the oxide and the electrical voltage RE-making it to some degree. Weak spots form, the voltage stress at the weak spots is higher, and it re-forms more at the weak spots. So eventually the oxide un-forms down to a voltage resisting level that the applied voltage will repair, for as long as the voltage and electrolyte chemistry can repair it.
Using something with an electro cap in it in a way that does not get it hot enough to outrun the re-forming process is the best way to get long life. Sticking the equipment in a closet unpowered is the same as leaving the capacitors unused. The oxide has no competing repair process for the inevitable deterioration. Electros last longer if they have a voltage applied. Overheating them can overwhelm that process.
As for the question of
That said I've serviced amplifiers with 5yr old aluminum electro's that were knocked way out of whack, and nice old amps from the 40's and 50's that had caps that looked like miniature toilet paper tubes dipped in wax that were spot on
Capacitor making changes over time. The electrolyte chemistry, foil thickness, and other issues are different with new caps and caps from the 40s and 50s. There is also the "survivor effect". You only see amps with surviving caps. To make a comparison, you'd have to know the history of the units being serviced, and compare the manufacturing processes. A lot of progress in modern manufacturing is to make things last as long as they have to, and to not spend money on making them last longer. Sad but true, and one consequence of what I call "MBA Disease" in businesses. Some caps are effectively immortal just because they are. Some caps die early. You definitely see the recent failures because there are more units with them and more units surviving to be repaired. The weak brother units from the 40s and 50s are all in landfills, or rebuilt.
