The robustness of complex biological processes in the face of environmental and genetic perturbations is a key biological trait. However, while robustness has been extensively studied, little is known regarding the fragility of biological processes. Here, we have examined the susceptibility of DNA replication and repair processes mediated by the proliferating cell nuclear antigen (PCNA). Using protein directed evolution, biochemical, and genetic approaches, we have generated and characterized PCNA mutants with increased affinity for several key partners of the PCNA-partner network. We found that increases in PCNA-partner interaction affinities led to severe in vivo phenotypic defects. Surprisingly, such defects are much more severe than those induced by complete abolishment of the respective interactions. Thus, the subtle and tunable nature of these affinity perturbations produced different phenotypic effects than realized with traditional "on-off" analysis using gene knockouts. Our findings indicate that biological systems can be robust to one set of perturbations yet fragile to others.