Cells must interpret environmental information that often changes over time. In our experiment, we systematically monitored the growth of yeast cells under various frequencies of oscillating osmotic stress. Growth was severely inhibited at a particular resonance frequency, at which cells show hyperactivated transcriptional stress responses. This behavior represents a sensory misperception: The cells incorrectly interpret oscillations as a staircase of ever-increasing osmolarity. The misperception results from the capacity of the osmolarity-sensing mitogen-activated protein kinase (MAPK) network to retrigger with sequential osmotic stresses. Although this feature is critical for coping with natural challenges, such as continually increasing osmolarity, it results in a trade-off of fragility to non-natural oscillatory inputs that match the retriggering time. These findings demonstrate the value of non-natural dynamic perturbations in exposing hidden sensitivities of cellular regulatory networks.