I did another full run on the static structure analysis, and two errors actually appear at the end of it. Sorry that I did not bring both up last time. The second error, apart from the one saying not converge, is that: Element 4730 located in Body "Solid" (and maybe other elements) has become highly distorted. You may select the offending object and/or geometry via RMB on this warning in the Messages window. Excessive distortion of elements is usually a symptom indicating the need for corrective action elsewhere. Try incrementing the load more slowly (increase the number of substeps or decrease the time step size). You may need to improve your mesh to obtain elements with better aspect ratios. Also consider the behavior of materials, contact pairs, and/or constraint equations. If this message appears in the first iteration of first substep, be sure to perform element shape checking. Named Selections for the offending element can be created via the Identify Element Violations property on the Solution Information Object.
The deformation graph is very distorted, with some elements deformed like 100 meters... So, I think it might still be the problem with defining the contact, which is kind of weird, as the modal analysis says the other way.