Graphene and similar semi-metals are known to transform into insulators under an external time-periodic electric field. This phenomenon, which is essential in the field of Floquet Topological Insulators, is traditionally understood as equivalent to the opening of a spectral gap. In most PDE (continuum) models of these materials, however, the conjecture is that there are no such gaps. How do we reconcile these seemingly contradictory statements? We show that the periodically-driven Schrödinger equation possesses an “effective gap” – a novel and physically relevant generalization of a spectral gap. Adopting a broader perspective, we study the influence of periodic driving on a broad class of Hamiltonians. A spectrally-local notion of stability is formulated and proven, using methods from periodic homogenization theory.