  We develop a theory of topological transitions in a Floquet topological
insulator, using graphene irradiated by circularly polarized light as a
concrete realization. We demonstrate that a hallmark signature of such
transitions in a static system, i.e. metallic bulk transport with conductivity
of order $e^2/h$, is substantially suppressed at some Floquet topological
transitions in the clean system. We determine the conditions for this
suppression analytically and confirm our results in numerical simulations.
Remarkably, introducing disorder dramatically enhances this transport by
several orders of magnitude.
