  As galaxies evolve, they must enrich and exchange gas with the surrounding
medium, but the timing of these processes and how much gas is involved remain
poorly understood. In this work, we leverage metals as tracers of past gas
flows to constrain the history of metal ejection and redistribution in M31.
This roughly $L*$ galaxy is a unique case where spatially resolved measurements
of the gas-phase and stellar metallicity, dust extinction, and neutral ISM gas
content are all available, enabling a census of the present metal mass. We
combine spatially resolved star formation histories from the Panchromatic
Hubble Andromeda Treasury survey with a metal production model to calculate the
history of metal production in M31. We find that $1.8\times10^9 \, M_\odot$ of
metals, or 62\% of the metal mass formed within $r < 19 \,\mathrm{kpc}$, is
missing from the disk in our fiducial model, implying that the M31 disk has
experienced significant gaseous outflows over its lifetime. Under a
conservative range of model assumptions, we find that between 3\% and 88\% of
metals have been lost ($1.9\times10^7 - 6.4\times10^9 \, M_\odot$), so metals
are missing even when all model parameters are chosen to favor metal retention.
We show that the missing metal mass could be harbored in M31's CGM if the
majority of the metals reside in a hot gas phase. Finally, we find that some
metal mass produced in the past 1.5 Gyr in the central $\sim5 \,\mathrm{kpc}$
has likely been redistributed to larger radii within the disk.
