The use of high-performance polymeric microfibres in enhancing the ductility of cementitious composites is widespread. A vivid example is the application of strain-hardening cement-based composites (SHCCs) in the construction industry. However, there are a few challenges which need to be addressed with respect to material design. For instance, the ductility of SHCC diminishes under alternating tension-compression loading, where the fibres lose their crack-bridging capacity due to specific damage mechanisms. The damage development and its influence on crack-bridging capacity have been studied in previous works by the authors. The paper at hand focuses on the influence of crack width on the crack-bridging capacity of polymeric microfibres in conjunction with the number of cycles in an alternating tension-compression regime with different cyclic compressive force levels. It shows that bridging capacity can be markedly influenced by crack width: an increase in crack width leads to more severe damage to the fibres and thus to lower crack-bridging capacity. Then, after analysing the specimens by means of electron microscopy, a hypothesis is presented to address the effect of crack width on damage development. Finally, a simple approach is proposed for estimating the influence of different parameters on fibre degradation.