This paper evaluates and discusses the performance of unreinforced masonry buildings accounting for cumulated damage during a seismic sequence. The considered case study is located in the Italian region of Irpinia. A single building, belonging to one of the most common construction typologies of the area, is selected and a numerical model is developed using an equivalent-frame strategy. A seismic sequence impacting the building compatible with the main event of the Irpinia earthquake of 1980 is generated. Nonlinear dynamic analysis of the building subjected to the seismic sequence is then carried out to identify the performance state attained after each event, also accounting for the damage cumulated during the entire sequence. Nonlinear static and dynamic analyses are also performed to derive fragility curves corresponding to the damage states attained after each event, with the aim of performing risk studies.