Until comparatively recently, capacitors -especially in large sizes - were generally rated for a few (2-3) thousand hours at 85degree service. Most major manufacturers usually rate lifetime of electrolytic caps as the point at which ESR doubles - partly because this massively increases losses and so the performance slides off the page soon after.
Reservoir caps run warm inside due to the high ripple currents they endure, and consequent I^2 *ESR losses (Joule heating). Electrolytic cap life essentially halves for every 10degreeC rise in internal temp, pretty much after Arrhenius' Equation.
Anyway, say a given electrolytic reservoir cap is rated for 3000hrs life at 85degC. This is a common value - do check the datasheet for this info- it's normal-to-good performance BTW although it looks horrific since 3000hrs ~ only 5months. Let's look at that: say the cap runs at 45degC - about as hot as you can comfortably touch indefinitely - when inside a piece of running equipment; but it is the capacitor's internal temperature that matters, which will be above that of the case.
Then our example's rated performance should last about 2^[85-45) / 10] or 2^4 = 16 x the rated life. That's 16x3000hrs or say 6 years. You might similarly calculate a 105degC, 3000-hr rated part to last over 20yrs; but the truth is the terminal seals will likely fail first. Useful life - moot; check them after a decade
Either way still gives an first expectation of life of around 6 -10yrs continuously powered. It doesnt say more won't happen, just backs up recommendation to review (service)
Hence why a handful of conscientious manufacturers bother to recommend service between 7-10yrs. It's based on good physics, not revenue
