The accumulation of plastic deformations during an intense earthquake may cause structural failures at deformations significantly smaller than those that can be developed under monotonic load. However, there is evidence that, under certain circumstances, the response of a single parameter may not be a good indicator of structural damage. Likewise, most of the seismic regulations, including the Mexican standards, establish their criteria considering the occurrence of strong earthquakes with a very little probability of occurrence, but do not consider if intense earthquake affects the building frequently and, therefore, cumulative damage due to the occurrence of several earthquakes during the life span of the structure is not taken into account explicitly. This cumulative damage is especially important in places like Mexico City, where intense and long-duration earthquakes occur every 10–20 years. To study the issues that Mexico City must face to increase its seismic resilience, in this article, we present an analysis of the dissipated plastic energy demands in Mexico City during the earthquake of 19 September 2017, and the cumulative damage due to recent intense earthquakes that affect the city.