Although long-span suspension bridges play a vital role in the transportation infrastructure, their resistance to disproportionate collapse resulting from locally induced damage has not yet been adequately investigated. In this study, computational simulation is used to shed light on how a prototype long-span suspension bridge responds to sudden loss of suspenders. Several scenarios were considered, with a focus on the total number of suspenders lost, their locations, and mode of removal. An increasing number of suspenders were removed either sequentially (i.e., one at a time) or simultaneously (i.e., multiple suspenders removed at the same time) until progressive collapse of the bridge was triggered. The simulation results showed that the bridge exhibited increasing levels of damage as the number of removed suspenders increased, and that the most critical location for suspender removal was near the middle of the bridge. It is shown that the sequential loss of a group of suspenders led to bridge responses that are almost identical with the simultaneous loss of the same group of suspenders. It is also argued that suspension bridges like the prototype system under consideration are highly robust.