  The Ly$\alpha$ forest (LAF) at $z>5$ probes the thermal and reionization
history of the intergalactic medium (IGM) and the nature of dark matter, but
its interpretation requires comparison to cosmological hydrodynamical
simulations. At high-$z$, convergence of these simulations is more exacting
since transmission is dominated by underdense voids that are challenging to
resolve. With evidence mounting for a late end to reionization, small
structures down to the sub-kpc level may survive to later times than
conventionally thought due to the reduced time for pressure smoothing to impact
the gas, further tightening simulation resolution requirements. We perform a
suite of simulations using the Eulerian cosmological hydrodynamics code Nyx,
spanning domain sizes of 1.25-10 $h^{-1}$ Mpc and 5-80 $h^{-1}$ kpc cells, and
explore the interaction of these variables with the timing of reionization on
the properties of the matter distribution and the simulated LAF at $z=5.5$. In
observable Ly$\alpha$ power, convergence within 10% is achieved for $k< 0.1$
s/km, but larger $k$ shows deviation of up to 20 percent. While a later
reionization retains more small structure in the density field, because of the
greater thermal broadening there is little difference in the convergence of LAF
power between early ($z=9$) and later ($z=6$) reionizations. We conclude that
at $z\sim5.5$, resolutions of 10 kpc are necessary for convergence of LAF power
at $k<0.1$ s/km, while higher-$k$ modes require higher resolution, and that the
timing of reionization does not significantly impact convergence given
realistic photoheating.
