© 2014 The Authors. 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*= 108.5-1010.5M), with only ~20 per cent 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 haloes quench their satellites more efficiently. These results extend trends seen previously in more massive host haloes and for higher satellite masses. Taken together, it appears that galaxies with stellar masses larger than about 108M 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 stellarmasses (<108M), 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.