Masonry arch bridges, despite their historical and infrastructural significance, are increasingly vulnerable due to ageing, rising traffic loads, and the growing frequency of extreme environmental events. This vulnerability highlights the need for effective preservation methods, allowing their evaluation and ensuring their longevity. This research focuses on enhancing the resilience of masonry arch bridges by examining failure mechanisms and investigating critical damage states that are correlated to these mechanisms. A case study of a multi-span, multi-ring railway bridge in Catalonia, Spain, illustrates the complexities involved in analyzing real-world masonry structures. Through limit analysis, the study evaluates the influence of the backing height and the effects of different damage scenarios on observed structural behavior and potential failure patterns. The influence of ring separation at different positions is examined into detail. The insights derived from this analysis can contribute to the development of data-driven inspection and maintenance strategies aimed at preventing collapse and contributing to a sustainable preservation of masonry arch bridges.