Cells delayed in metaphase with intact mitotic spindles undergo cohesion fatigue, where sister chromatids separate asynchronously, while cells remain in mitosis. Cohesion fatigue requires release of sister chromatid cohesion. However, the pathways that breach sister chromatid cohesion during cohesion fatigue remain unknown. Using moderate-salt buffers to remove loosely bound chromatin cohesin, we show that "cohesive" cohesin is not released during chromatid separation during cohesion fatigue. Using a regulated protein heterodimerization system to lock different cohesin ring interfaces at specific times in mitosis, we show that the Wapl-mediated pathway of cohesin release is not required for cohesion fatigue. By manipulating microtubule stability and cohesin complex integrity in cell lines with varying sensitivity to cohesion fatigue, we show that rates of cohesion fatigue reflect a dynamic balance between spindle pulling forces and resistance to separation by interchromatid cohesion. Finally, while massive separation of chromatids in cohesion fatigue likely produces inviable cell progeny, we find that short metaphase delays, leading to partial chromatid separation, predispose cells to chromosome missegregation. Thus, complete separation of one or a few chromosomes and/or partial separation of sister chromatids may be an unrecognized but common source of chromosome instability that perpetuates the evolution of malignant cells in cancer.