This work evaluates the damage to and collapse of a set of buildings in the September 2017 earthquake in Mexico City; these buildings were also subjected to the September 1985 Mexico City earthquake. These buildings were located in the area of the highest rate of damage or collapse in 1985, but buildings exhibiting significant damage or collapse in 2017 did not possess any retrofitting. The spectral demands for these buildings, based on typical records registered in the earthquakes of 1985 and 2017, were not much different, suggesting the need to explain why the buildings that collapsed suffered severe damage in 2017 but not in 1985. This building behavior was analyzed using a seismic damage index Id, previously proposed by the author, which considers the effect of cumulative damage. The results indicated that the observed damage to and collapse of these buildings in the September 2017 earthquake can be explained by the effect of cumulative seismic damage. Recommendations are given for possible improvements to the seismic building codes in Mexico.