Auto windows - 2012 S3 Sport back

Does it work the other way? So when you close the windows pulling the switch briefly to the second stop - does the window automatically close all the way? If not as these are two stage switches I would guess the switch is broken so only working on the first stop.
If you've recently disconnected your battery the one-touch open and close function must be reactivated as follows
Pull and hold the electric window switch until the window is fully closed.
Release the switch and then pull it again for at least one second.

As Pluves said, just pull the switch until the window closes and hold it there for a few seconds. Do the same with the window down for good measure. This should 're-calibrate' things and hopefully work. It's happened to me a couple of times before - easy fix.