Non-intrusive speech intelligibility metrics are based solely on the corrupted speech information and a prior model of the speech signal in a given representation. As such, any sources of variability not taken into account by the model will affect the metric's performance. In this paper, we investigate two sources of variability in the auditory-inspired model used by the speech-to-reverberation modulation energy ratio (SRMR) metric, namely speech content and pitch, and propose two updates that aim to reduce the variability caused by these sources. First, we limited the dynamic range of the energies in the modulation spectrum bands in order to reduce the effect of speech content and speaker variability. Second, the range of the modulation filter bank was modified to reduce the variability due to pitch. Experimental results show that the updated metric presents higher performance and lower variability relative to the original SRMR when assessing speech intelligibility in noisy and reverberant environments, as well as outperforms several standard intrusive and non-intrusive benchmark metrics.