Help understanding supercapacitor design

I'm having trouble wrapping my head around the materials and operation of supercapacitors. Given the fact that supercapacitors are built using 2 electrodes (conductive) with an activated carbon or graphene coating (also conductive), with an electrolyte in between (which is also conductive), how does the capacitor maintain a charge and not self discharge? It seems that all materials between the electrodes conduct electricity, which should short the electrodes.

This has been bothering me for a few days, and I've yet to find an explanation.

Thanks in advance!

Wikipedia has a brief description, together with a load of references.
https://en.wikipedia.org/wiki/Supercapacitor
On the basis of that, together with a look at the numerous references, you should be able to come to grips with it. If it has already bothered you for a few days, then a few hours reading up on some of the physics may bother you for a few more days,
cheers,
Richard