1) Theres something weird because it is not just a shift but a change in the character.
2) Strictly speaking, FEM gives correct results only at meshing frequency. The closest frequencies may reuse the mesh, particularly in lower band, if there are no peculiarities, like cutoffs and resonances. in that way solve bands separately, or in new HFSS versions set multiple frequencies above and below the peculiarities.
3) Use discrete sweep, check that there is no mistake and it is really discrete.
4) Set number of passes to 15-20, and the convergence to 0.05. The default is only good for simple straight lines.
Try 2nd order or mixed order solver.