This is one of those questions where the answer is always, "it depends."
Loss of electrolyte over time due to imperfect sealing around the terminals is a major cause of "death by senility" in aluminum electrolytic capacitors. This failure mechanism causes ESR to rise - sometimes dramatically - and there is no curing it. So, a good first pass test of any NOS (New Old Stock) capacitor is to measure its ESR. And how do you know if the ESR is too high or still ok? Well, that very much depends on the capacitor, but a general purpose elko will have a dissipation factor, DF, which is the ratio of ESR to Xc, of around 10-20% (0.1-0.2). An elko is usually considered EOL (end of life) when DF has doubled.
For example, a 100uF capacitor will have a capacitive reactance, Xc, at 1kHz (a common frequency used to test ESR) of 1.59 Ohms, so a good capacitor should have an ESR of between 0.159 and 0.318 Ohms (ie - 10% to 20% of Xc), while an ESR of >0.6 Ohms would be suspect.
The other age-related failure mechanism is a loss of the dielectric layer over time which causes the DC leakage current to increase, perhaps to the point of causing the capacitor to overheat and possibly even explode. However, this failure mechanism can be reversed by merely applying a slowly increasing voltage to the capacitor over time which re-forms the dielectric layer. How slowly? No prizes if you guessed the answer is, "it depends...," but I've seen recommendations as wide as going from 0V to rated voltage at the rate of 1 minute per month of storage to 1 hour per year of storage; in my experience it doesn't really matter, just keep an eye on the actual current flowing through the capacitor after each increase in voltage and wait until it has dropped below a few hundred microamps before increasing the voltage again in steps/amounts no more than 1% of the capacitor's rated voltage.