Cells can maintain their functions despite fluctuations in intracellular parameters, such as protein activities and gene expression levels. This commonly observed biological property of cells is called robustness. On the other hand, these parameters have different limitations, each reflecting the property of the subsystem containing the parameter. The budding yeast cell cycle is quite fragile upon overexpression of CDC14, but is robust upon overexpression of ESP1. The gene products of both CDC14 and ESP1 are regulated by 1ratio1 binding with their inhibitors (Net1 and Pds1), and a mathematical model predicts the extreme fragility of the cell cycle upon overexpression of CDC14 and ESP1 caused by dosage imbalance between these genes. However, it has not been experimentally shown that dosage imbalance causes fragility of the cell cycle. In this study, we measured the quantitative genetic interactions of these genes by performing combinatorial "genetic tug-of-war" experiments. We first showed experimental evidence that dosage imbalance between CDC14 and NET1 causes fragility. We also showed that fragility arising from dosage imbalance between ESP1 and PDS1 is masked by CDH1 and CLB2. The masking function of CLB2 was stabilization of Pds1 by its phosphorylation. We finally modified Chen's model according to our findings. We thus propose that dosage imbalance causes fragility in biological systems.