Some years passed i see - but maybe someone will use it :)
I had this problem too and it was solved by cleaning potentiometer on X (up and down) axis of Left Stick.
Its a small disk like thingy inside left stick.
This video shows it preety good https://www.youtube.com/watch?v=4AkDIzKqmYY - however i didnt replaced the part but cleaned it with tissue paper. There was some dirt or rust, i dont know.
However be careful because as told in video you can broke it easily.
It really sound strange but it worked - i cleaned it about 2 weeks ago and the problem vanished :).