Experiments in vivo have shown that the reliability in response to fluctuating inputs is high, whereas constant inputs produced unreliable responses. Simulations using stochastic Hodgkin-Huxley neuron models confirmed the experimental findings. It was argued that the fluctuations present in the time-varying inputs become the main force driving the cell towards a spike, attenuating the influence of the ion channels stochasticity and increasing reliability. In this work I put forward an alternative explanation, which is relevant for the neuron models near a subcritical Hopf bifurcation. Such models, termed resonators, exhibit damped sub-threshold oscillations, which set the eigenfrequency of the membrane. All resonators, in particular the Hodgkin-Huxley model, are provably sensitive to those spectral components of their inputs, which are close to the eigenfrequency. I suggest that the spectral content around the eigenfrequency is the main factor leading to high reliability. A signal possessing this spectral content elicits a relatively reliable response. Constant input is an extreme particular case of a signal lacking these spectral components, which will lead to low reliability. To test the hypothesis fluctuating signals constructed as the low-pass Gaussian white noise are band-pass and band-stop filtered around the eigenfrequency of the model, which is determined by analyzing the sub-threshold activity. The band-pass filtered signals elicited responses with high reliability measure values very close to those produced by the original inputs. In contrast, the band-stop filtered signals produced very unreliable responses with the reliability measure values only slightly exceeding those produced by the constant stimuli. These results confirm the frequency-dependence hypothesis, indicating that the spectral characteristics of the input signal have a crucial role in determining the temporal reliability and precision. A new robust measure of reliability is introduced.