  We investigate numerically how onsite disorder affects conduction in the
periodically driven Rice-Mele model, a prototypical realization of the Thouless
pump. Although the pump is robust against disorder in the fully adiabatic
limit, much less is known about the case of finite period time $T$, which is
relevant also in light of recent experimental realizations. We find that at any
fixed period time and nonzero disorder, increasing the system size $L\to\infty$
always leads to a breakdown of the pump, indicating Anderson localization of
the Floquet states. Our numerics indicate, however, that in a properly defined
thermodynamic limit, where $L/T^\theta$ is kept constant, Anderson localization
can be avoided, and the charge pumped per cycle has a well-defined value -- as
long as the disorder is not too strong. The critical exponent $\theta$ is not
universal, rather, its value depends on the disorder strength. Our findings are
relevant for practical, experimental realizations of the Thouless pump, for
studies investigating the nature of its current-carrying Floquet eigenstates,
as well as the mechanism of the full breakdown of the pump, expected if the
disorder exceeds a critical value.
