Giulio,
If you introduce the contacts near the ends of the springs, the deformation might become more symmetric. But as mentioned, it is more difficult to get a nonlinear analysis to converge, as the problem becomes more complex. The mesh becomes more important, for example. One strategy is to run the analysis as a "Quick check" (P-level 3 only) with a fine mesh.
And a possible explanation why the spring does not deform symmetrically, is simply that it does so also in reality.
/Mats