We investigate the effect of microwave-induced breakdown on the frequency responses of a class of metamaterials composed of planar sub-wavelength periodic structures. When breakdown occurs in such a structure, its frequency response changes based on the nature of the plasma created within its unit cell. We examine how the frequency responses of such periodic structures change as a result of creation of microwave-induced discharges within their unit cells. To do this, we examine single-layer metasurfaces composed of miniature LC resonators arranged in a 2-D periodic lattice. These metasurfaces are engineered to be opaque at microwave frequencies when operated at low power levels but can be made transparent if a localized discharge is created within the LC resonators. By measuring their transmission and reflection coefficients under high-power excitation in different conditions, the impact of breakdown on the frequency responses of these devices is determined. Several prototypes of such structures are examined both theoretically and experimentally. It is demonstrated that when breakdown occurs in air and at atmospheric pressure levels, the responses of such periodic structures can be predicted with a reasonable degree of accuracy. Additionally, when the unit cell of the metasurface is composed of two different resonators, breakdown is always observed to occur in both resonators despite their different topologies and local field enhancement factors. In such structures, the discharge in one resonator appears to be mediated by the one in the other.