  The analysis and interpretation of exoplanet spectra from time-series
observations remains a significant challenge to our current understanding of
exoplanet atmospheres, due to the complexities in understanding instrumental
systematics. Previous observations of the hot Jupiter WASP-31b using
transmission spectroscopy at low-resolution have presented conflicting results.
Hubble Space Telescope (HST) observations detected a strong potassium feature
at high significance (4.2\sigma), which subsequent ground-based
spectro-photometry with the Very Large Telescope (VLT) failed to reproduce.
Here, we present high-resolution observations (R>80,000) of WASP-31b with the
UVES spectrograph, in an effort to resolve this discrepancy. We perform a
comprehensive search for potassium using differential transit light curves, and
integration over the planet's radial velocity. Our observations do not detect K
absorption at the level previously reported with HST, consistent with the VLT
observations. We measure a differential light curve depth $\Delta F = 0.00031
\pm 0.00036$ using 40\AA\ bins centred on the planet's K feature, and set an
upper limit on the core line depth of $\Delta F \leq 0.007$ (3\sigma) at a few
times the resolution limit ($\approx0.24\AA$). These results demonstrate that
there are still significant limitations to our understanding of instrumental
systematics even with our most stable space-based instrumentation, and that
care must be taken when extracting narrow band signatures from low-resolution
data. Confirming exoplanet features using alternative instruments and
methodologies should be a priority, and confronting the limitations of
systematics is essential to our future understanding of exoplanet atmospheres.
