From the 3d visualization http://www.satflare.com/track.asp?q=25544#TOP (the right image with the red line indication the path of the ISS) it looks like always the ISS takes the same path. Is it the case?
It shows the orbit of the station around the earth as a red line. From this view, the position of the line is approximately fixed around the center of the earth, with the angle almost fixed with respect to the stars (inertial frames).
In this view, the earth turns to the right (west to east) underneath the path, causing the ISS to pass over ground farther to the west every orbit.
If the earth were a perfect sphere and alone in space, the orbital path in this view would not drift. But it does move over time. The largest contributor to the shift is the fact that the earth is not a sphere. The squished earth has more mass around the equator than it does near the poles. This asymmetry causes the orbital path to precess (east to west) at about 5 degrees per day$^1$. If you were in the same position relative to the earth and the stars, you would see the orbital plane rotate around Antarctica over the course of two and a half months.