  We present the lifetime star formation histories (SFHs) for six ultra-faint
dwarf (UFD; $M_V>-7.0$, $ 4.9<\log_{10}({M_*(z=0)}/{M_{\odot}})<5.5$) satellite
galaxies of M31 based on deep color-magnitude diagrams constructed from
\textit{Hubble Space Telescope} imaging. These are the first SFHs obtained from
the oldest main sequence turn-off of UFDs outside the halo of the Milky Way
(MW). We find that five UFDs formed at least 50\% of their stellar mass by
$z=5$ (12.6~Gyr ago), similar to known UFDs around the MW, but that 10-40\% of
their stellar mass formed at later times. We uncover one remarkable UFD,
\A{XIII}, which formed only 10\% of its stellar mass by $z=5$, and 75\% in a
rapid burst at $z\sim2-3$, a result that is robust to choices of underlying
stellar model and is consistent with its predominantly red horizontal branch.
This "young" UFD is the first of its kind and indicates that not all UFDs are
necessarily quenched by reionization, which is consistent with predictions from
several cosmological simulations of faint dwarf galaxies. SFHs of the combined
MW and M31 samples suggest reionization did not homogeneously quench UFDs. We
find that the least massive MW UFDs ($M_*(z=5) \lesssim 5\times10^4 M_{\odot}$)
are likely quenched by reionization, whereas more massive M31 UFDs ($M_*(z=5)
\gtrsim 10^5 M_{\odot}$) may only have their star formation suppressed by
reionization and quench at a later time. We discuss these findings in the
context of the evolution and quenching of UFDs.
