I get the warning "Convergence criteria (within line search) not satisfied due to eta limit, continuing superordinate iteration" during analysis, what does it mean?

It is a warning about the line search iterations. Line search method is explained in the Theory manual in chapter 4.5 page 180. This method only helps to stabilize the convergence process. Normally, the solution parameters are defined such that only 1-2 line search iterations are performed in each step. Thus, it is quite normal that it is not enough for this method to fully converge, but it is not a problem and the main important thing is that at the end each analysis step converges. This you can for instance check in the menu Data | Analysis progress information in ATENA 3D.