The close encounter of comet Siding Spring with Mars resulted in the formation of a dense transient ionization layer in the Martian upper atmosphere at altitudes between 80 and 120 km. Instruments on three spacecraft orbiting Mars detected the presence of this layer, as reported in previous publications. In this study, we reanalyzed the ionograms of the Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) instrument on Mars Express to get further insight about the recurrence of the layer. For this purpose, data from three periapsis passes of MARSIS that took place 5 h, 12 h, and 19 h after peak dust deposition are used. We found that the transient ionization layer was sustained at least for 19 h on the nightside and 12 h on the dayside. While the peak density of the layer on the nightside gradually decreases from orbit to orbit, it does not change much on the dayside. Some ionograms in all three orbits show two transient ionization layers that are separated by ~60 km in apparent altitude. These double layers occur preferentially in regions of strong vertical magnetic fields. The bottom layer of the double structure is probably an oblique echo due to reflections from ionization bulges (formed in regions of vertical magnetic fields) at altitudes of the transient ionization layer. Horizontal bifurcation of the original layer is considered as another plausible mechanism for explaining the double‐layer structure.