I had this sort of problem with my MK3 shortly after buying in Feb this year. Gave the dealer a quick call and he suggested it may be some sort of obstruction (possibly treesap due to wher ethe car had been parked) in the rubber seal and to try cleaning it then squirting with WD40.

Fixed the problem for me

I have cleaned the tires but they are successful. It goes up 1/3 and goes down, and at 2/3 it also goes down and I have to do it by tapping consecutively. 

I have an older 2007 Octavia mk2 and I had the same problem.  I ran the window all the way up and then pulled the up switch up three times in succession. then lowered the window all the way down and pushed the down switch three times in succession and it worked. You may want to give it a try?