Response inhibition, the intentional stopping of planned or initiated actions, is often considered a key facet of control, impulsivity, and self-regulation. The stop signal task is argued to be the purest inhibition task we have, and it is thus central to much work investigating the role of inhibition in areas like development and psychopathology. Most of this work quantifies stopping behavior by calculating the stop signal reaction time as a measure of individual stopping latency. Individual difference studies aiming to investigate why and how stopping latencies differ between people often do this under the assumption that the stop signal reaction time indexes a stable, dispositional trait. However, empirical support for this assumption is lacking, as common measures of inhibition and control tend to show low test-retest reliability and thus appear unstable over time. The reasons for this could be methodological, where low stability is driven by measurement noise, or substantive, where low stability is driven by a larger influence of state-like and situational factors. To investigate this, we characterized the split-half and test-retest reliability of a range of common behavioral and electrophysiological measures derived from the stop signal task. Across three independent studies, different measurement modalities, and a systematic review of the literature, we found a pattern of low temporal stability for inhibition measures and higher stability for measures of manifest behavior and non-inhibitory processing. This pattern could not be explained by measurement noise and low internal consistency. Consequently, response inhibition appears to have mostly state-like and situational determinants, and there is little support for the validity of conceptualizing common inhibition measures as reflecting stable traits.