Periodic structures can present wave phenomena that can be used to attenuate vibration in certain frequency bands. Periodic structures are usually divided into metamaterials (locally resonant structures) and phononic crystals (exhibiting Bragg scattering). More recently, topological phononics and metamaterials have emerged as more robust solutions, topologically protected against defects. Interface topological modes may be achieved via a combination of two periodic structures with geometrical or material differences. Interface modes can be localized at some specific regions of the structure. Robustness against variability and defects is achieved by the so-called topological protection. In the current study, we investigate the robustness of interface topological modes in rods (longitudinal vibrations) and we show that this robustness is frequency dependent and has different effects on the mode shape and frequency of the interface topological mode.