There are two effects here.
For once the breakdown strenght of air increases as the gap width decreases. That is predicted by Paschen's law
http://en.wikipedia.org/wiki/Paschen's_law
At a few µm you need more than 40 MV/m while for a gap between 1cm and 1m it's around 3MV/m.
The second effect was explained already by Baluncore. There are not many ions in a tiny air gap so you can't get much of a current.
It's actually possible to "glue" two pieces of plastic foil together with static charge and under the right conditions (no moisture in between the foils, smooth surface so the gap is really small) the foil will stick together for many years.
You probably know that a roll of plastic foil can become charged when it's unrolled. But most people don't realize that that charge was put on the foil in the factory. It's not produced when you unroll it. Equal amounts of positive and negative charge are trapped in the roll of foil causing very strong fields in the gaps between the layers, while the total net charge is zero. That roll can be sitting on a shelf for years without loosing it's charge.