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While there have been extensive studies of nonthermal atmospheric dielectric-barrier discharges (DBD), many key facets of their characteristics remain to be unraveled before their full understanding is achieved. One of the missing pieces in our current knowledge is the dependence of stable DBD production upon temporal characteristics of the applied voltage such as excitation frequency. In this contribution, we report a numerical investigation of the frequency range for the generation of stable DBD and that of likely mechanisms for disruption of DBD stability. We show that when the excitation frequency is too low, an irreversibly large mismatch of the rise-time occurs between the applied voltage and the memory voltage. It is demonstrated that this mismatch results in a rapid suppression of the gas voltage and as such, the generated DBD is quenched prematurely. Also, it is shown that when the excitation frequency is too high, most electrons produced in the plasma bulk become trapped in the interelectrode gap and are unable to reach the electrodes. As a result, the gas voltage increases without being contained adequately by a sizeable memory voltage. Again, this leads to premature plasma quenching. These observations highlight the importance of the dynamic balance between the applied voltage and the memory voltage in dielectric-barrier discharges. We compare the above issues in both a helium DBD and a nitrogen DBD and report that our findings of the two stability disruption mechanisms are generic in different DBD systems.