We study a structural model of individual bank defaults across the banking sector; banks are interconnected through their exposure to a common risk factor. The paper introduces a systemic risk measure based on the default frequency in the banking sector; this measure depends non-linearly on the factor's loadings, in contrast to previous systemic risk measures that depend linearly on loadings. We estimate loadings in the U.S. banking system over the course of the last 36 years; we find that they have considerably increased over time and identify four major regimes. Our measure shows that systemic risk became critical in the last of our four regimes, covering the most recent time period from 05/2007 to 09/2016. The empirical findings highlight that our measure complements existing systemic risk measures.