New vector contours from a DEM will never match the original contours. Actually, the sample you attached looks pretty good! The contour re-entries (the pointed tips in the valleys) especially tend to become clipped off.
This is because the new contours are created from a grid of elevation points, which in turn is created from the original contours using one of any number of algorithms. Some algorithms are better than others at creating grids that are close to the landscape that the original contours portray. The DEST algorithm used by Manifold is touted as being very good at this, though my experience is that there are still some clipped valleys here and there.
What to do? Depending on what software you're using, you may be able to go into the problem areas and manually add extra elevation points, and then recreate the grid. It may even be as simple as making sure there are extra vertices within the contours themselves. Again, the exact how-to depends on your software.