  A well-studied possibility is that dark matter may reside in a sector
secluded from the Standard Model, except for the so-called photon portal:
kinetic mixing between the ordinary and dark photons. Such interactions can be
probed at dark matter direct detection experiments, and new experimental
techniques involving detection of dark matter-electron scattering offer new
sensitivity to sub-GeV dark matter. Typically however it is implicitly assumed
that the dark matter is not altered as it traverses the Earth to arrive at the
detector. In this paper we study in detail the effects of terrestrial stopping
on dark photon models of dark matter, and find that they significantly reduce
the sensitivity of XENON10 and DAMIC. In particular we find that XENON10 only
excludes masses in the range (5-3000) MeV while DAMIC only probes (20-50) MeV.
Their corresponding cross section sensitivity is reduced to a window of cross
sections between $(5\times 10^{-38}-10^{-30})~{\rm cm}^{2}$ for XENON10 and a
small window around $\sim 10^{-31}~{\rm cm}^{2}$ for DAMIC. We also examine
implications for a future DAMIC run.
