The search for rocky planet atmospheres with JWST has focused on planets transiting M dwarfs. Such planets have favorable planet-to-star size ratios, enhancing the amplitude of atmospheric features. Since the expected signal strength of atmospheric features is similar to the single-transit performance of JWST, multiple observations are required to confirm any detection. Here, we present two transit observations of the rocky planet GJ 1132 b with JWST NIRSpec G395H, covering 2.8–5.2 μm. Previous Hubble Space Telescope WFC3 observations of GJ 1132 b were inconclusive, with evidence reported for either an atmosphere or a featureless spectrum based on analyses of the same data set. Our JWST data exhibit substantial differences between the two visits. One transit is consistent with either an H2O-dominated atmosphere containing ∼1% CH4 and trace N2O (
χ
ν
2
=
1.13
) or stellar contamination from unocculted starspots (
χ
ν
2
=
1.36
). However, the second transit is consistent with a featureless spectrum. Neither visit is consistent with a previous report of HCN. Atmospheric variability is unlikely to explain the scale of the observed differences between the visits. Similarly, our out-of-transit stellar spectra show no evidence of changing stellar inhomogeneity between the two visits—observed 8 days apart, only 6.5% of the stellar rotation rate. We further find no evidence of differing instrumental systematic effects between visits. The most plausible explanation is an unlucky random noise draw leading to two significantly discrepant transmission spectra. Our results highlight the importance of multivisit repeatability with JWST prior to claiming atmospheric detections for these small, enigmatic planets.