Audio signal processing methods based on deep neural networks (DNNs) are typically trained only at a single sampling frequency (SF) and therefore require signal resampling to handle untrained SFs. However, recent studies have shown that signal resampling can degrade performance with untrained SFs. This problem has been overlooked because most studies evaluate only the performance at trained SFs. In this paper, to assess the robustness of DNNs to SF changes, which we refer to as the SF-independent (SFI) property, we propose three metrics to quantify the SFI property on the basis of local equivariance error (LEE). LEE measures the robustness of DNNs to input transformations. By using signal resampling as input transformation, we extend LEE to measure the robustness of audio source separation methods to signal resampling. The proposed metrics are constructed to quantify the SFI property in specific network components responsible for predicting time-frequency masks. Experiments on music source separation demonstrated a strong correlation between the proposed metrics and performance degradation at untrained SFs.