  We study the breakdown of diffusive hydrodynamics in holographic systems dual
to neutral dilatonic black holes with extremal near horizon geometries
conformal to AdS$_2\times\,$R$^2$. We find that at low temperatures by tuning
the effective gauge coupling constant in the infra-red, the lowest
non-hydrodynamic mode, which collides with the charge diffusive mode and sets
the scales at which diffusive hydrodynamics break down, could be either an
infra-red mode or a slow mode, resulting in different scaling behaviors of the
local equilibrium scales. We confirm that the upper bound for the charge
diffusion constant is always satisfied using the velocity and timescale of
local equilibration from the pole collision. We also examine the breakdown of
hydrodynamics at general temperature and find that the convergence radius has
nontrivial dependence on temperature, in addition to the effective gauge
coupling constant.
