We study dwarf satellite galaxy quenching using observations from the Geha et al . ( 2012 ) NSA/SDSS catalog together with \Lambda CDM cosmological simulations to facilitate selection and interpretation . We show that fewer than 30 \% of dwarfs ( M _ { \star } \simeq 10 ^ { 8.5 - 9.5 } M _ { \odot } ) identified as satellites within massive host halos ( M _ { host } \simeq 10 ^ { 12.5 - 14 } M _ { \odot } ) are quenched , in spite of the expectation from simulations that half of them should have been accreted more than 6 Gyr ago . We conclude that whatever the action triggering environmental quenching of dwarf satellites , the process must be highly inefficient . We investigate a series of simple , one-parameter quenching models in order to understand what is required to explain the low quenched fraction and conclude that either the quenching timescale is very long ( > 9.5 Gyr , a “ slow starvation ” scenario ) or that the environmental trigger is not well matched to accretion within the virial volume . We discuss these results in light of the fact that most of the low mass dwarf satellites in the Local Group are quenched , a seeming contradiction that could point to a characteristic mass scale for satellite quenching .