Are you asking why the resonant frequency shifts at oblique angles?  Some FSS's operate due to element resonance and these types should have a pretty stable frequency response.  Other FSS's work due to interaction between adjacent elements.  In this case frequency can shift because there is a phase matching condition that has to happen between the applied wave and the mode travelling along the FSS.  Essentially the tangential component of the incident wave vector has to equal the propagation constant of the mode along the FSS.  These are normally not equal, but the FSS is a grating that can make up the difference.  However, when the angle of incidence changes, the tangential component of the incident wave vector changes, and thus the phase matching condition changes.  This shifts the response of the FSS to a different frequency.

Try visualizing the electromagnetic field and compare to on and off the glitch you are seeing.  This may give you a clue about what is happening.

 In addition to Dr. Rumpf answer, Aperture type FSS are highly insensitive to incident angles due to the size of the unit cell. Unit cell sizes are approximately equal to the half of the resonant wavelength. To decrease the effect of variation in resonant frequency try applying the miniaturization techniques. Miniaturization of unit cell allows planar phase front for maximum number of elements in the FSS screen at oblique angle of incidences also.