  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 $\mu$m. Previous HST 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 dataset. Our JWST data
exhibit substantial differences between the two visits. One transit is
consistent with either a H$_2$O-dominated atmosphere containing ~1% CH$_4$ and
trace N$_2$O ($\chi^{2}_{\nu}$ = 1.13) or stellar contamination from unocculted
starspots ($\chi^{2}_{\nu}$ = 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 multi-visit repeatability with JWST prior to claiming atmospheric
detections for these small, enigmatic planets.
