You have two components at work:
One is due to the true DC leakage current of the dielectric itself. The dielectric is present as the result of an electrochemical reaction, one which is still ongoing. The voltage rating of the dielectric corresponds to the voltage it was "formed" at; over time, this gradually dissolves, reducing the "formed" voltage. In normal operation, just enough leakage current is drawn to oppose this inverse reaction, and operation remains nice and stable.
If equipment is left unpowered for a very long time (decades), the "formed" voltage decays, and leakage can be so high that capacitors heat up, produce hydrogen gas (which is held internally, increasing pressure), and in very bad cases, breaking the seal or relief, or causing an explosion. (Of note, old style metal cans were sealed without relief cuts, so they tended to go
sky-high in such cases. This is not an exaggeration.)
If you have a very slowly changing voltage (like, days to years), more leakage will be drawn during the higher peaks, and less during the lower valleys, but ultimately being about the same average.
The second part is dynamic, an AC phenomenon that can manifest as leakage. This is dielectric absorption. This acts like a smaller capacitor (some percent of nominal), connected in parallel with the nominal capacitor through a very large resistance. The time constant is on the order of minutes to days, so the equivalent resistance might be gigaohms for typical parts.
For this reason, you must make sure to "soak" the capacitor at exactly the nominal voltage, for an extended period of time, and monitor the leakage after that.
A notable case is the LT appnote about low noise: AN-83
http://cds.linear.com/docs/en/application-note/an83f.pdfThey used wet-slug tantalum capacitors (these use something like gelled sulfuric acid for electrolyte -- good to much higher temperatures than the gunk they stuff in aluminum electrolytics!), which cost something like 50 bucks a pop, and exhibited a week-ish "soak" period before they could finally be selected for least "true DC" leakage.
Tim