I'm not using NX 6 so could not upload a part file that you could open and inspect; but it is easy to create. Start the swept command (in NX 7.5 it can be found at Insert -> Sweep -> Swept, if I remember correctly it is the same in NX 6), pick your section curves, then your guides (make sure you have 2 separate guide strings in your list, do not pick the 2 curves as Guide 1). Other options per the attached jpg, almost all of which are the default options; the only one worthy of note is that I used Preserve Shape. Your input section has sharp corners which I assume you want to keep throughout the sweep. If you turn off this option, NX will approximate your section with splines, which in certain circumstances can lead to unexpected/undesired results.
It does not follow the curve because the curve isn't fully selected .
In the attached image i have double clicked the upper intersection point ( shown), the intersection point is then edited showing what curves are intersected, in this case it's only the first one. ( select the remaining ones)
