We present the star formation histories (SFHs) of 20 faint M31 satellites (-12 ≲ M V ≲-6) that were measured by modeling sub-horizontal branch 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 (τ ∼ 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 ⪆-6 would help quantify the relative contributions of reionization and environment to quenching of the lowest-mass satellites.