We present the star formation histories (SFHs) of 20 faint M31 satellites ($-12 lesssim M_V lesssim -6$) that were measured by modeling sub-horizontal branch (HB) depth color-magnitude diagrams constructed from Hubble Space Telescope (HST) imaging. Reinforcing previous results, we find that virtually all galaxies quenched between 3 and 9 Gyr ago, independent of luminosity, with a notable concentration $3-6$ Gyr ago. This is in contrast to the Milky Way (MW) satellites, which are generally either faint with ancient quenching times or luminous with recent ($<3$ Gyr) quenching times. We suggest that systematic differences in the quenching times of M31 and MW satellites may be a reflection of the varying accretion histories of M31 and the MW. This result implies that the formation histories of low-mass satellites may not be broadly representative of low-mass galaxies in general. Among the M31 satellite population we identify two distinct groups based on their SFHs: one with exponentially declining SFHs ($tau sim 2$ Gyr) and one with rising SFHs with abrupt quenching. We speculate how these two groups could be related to scenarios for a recent major merger involving M31. The Cycle 27 HST Treasury survey of M31 satellites will provide well-constrained ancient SFHs to go along with the quenching times we measure here. The discovery and characterization of M31 satellites with $M_V gtrsim -6$ would help quantify the relative contributions of reionization and environment to quenching of the lowest-mass satellites.
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