  Using the Sloan Digital Sky Survey, we examine the quenching of satellite
galaxies around isolated Milky Way-like hosts in the local Universe. We find
that the efficiency of satellite quenching around isolated galaxies is low and
roughly constant over two orders of magnitude in satellite stellar mass
($M_{*}$ = $10^{8.5}-10^{10.5} \, M_{\odot}$), with only $\sim~20\%$ of systems
quenched as a result of environmental processes. While largely independent of
satellite stellar mass, satellite quenching does exhibit clear dependence on
the properties of the host. We show that satellites of passive hosts are
substantially more likely to be quenched than those of star-forming hosts, and
we present evidence that more massive halos quench their satellites more
efficiently. These results extend trends seen previously in more massive host
halos and for higher satellite masses. Taken together, it appears that galaxies
with stellar masses larger than about $10^{8}~M_{\odot}$ are uniformly
resistant to environmental quenching, with the relative harshness of the host
environment likely serving as the primary driver of satellite quenching. At
lower stellar masses ($< 10^{8}~M_{\odot}$), however, observations of the Local
Group suggest that the vast majority of satellite galaxies are quenched,
potentially pointing towards a characteristic satellite mass scale below which
quenching efficiency increases dramatically.
