Modulation of an oscillator is crucial for its application in communication devices. While the output power and linewidth of single magnetic tunnel junction-based spin-torque oscillators (MTJ-STO) are not yet adequate for practical uses, the synchronization of such devices can overcome these limitations. Here, we investigate the modulation behavior of a parametrically synchronized MTJ-STO and show experimentally that modulation of the synchronized state preserves synchronization as long as the modulation frequency, integral(mod), is above a characteristic frequency, integral(unlock). The unlocking frequency increases with the modulation amplitude in agreement with analytical estimates and numerical simulations. These phenomena are described as a non-resonant unlocking mechanism, whose characteristics are directly related to inherent parameters of the oscillator.