Nanoscale dielectric resonator antennas (DRAs) are promising elements for constructing the next generation of efficient and compact optical devices. Their efficient light manipulation capability underpinned by electric and magnetic resonances at visible frequencies is appealing for optical metasurfaces with various functions such as anomalous re ection, polarization conversion and surface plasmon coupling. To realize these functions, the resonance properties of the individual DRA elements are of critical importance. In this paper, we study the resonance breakdown of nanoscale cylindrical DRAs on metallic substrates. By gradually increasing the relative permittivity of DRAs on a metallic ground plane from low to high values, we observe two types of resonance breakdown and on that basis we can define a permittivity range for efficient resonance. More specifically, the resonance breakdown occuring at low DRA permittivities is a result of weak confinement and excessive radiation loss. The resonance breakdown at high DRA permittivities is a result of an elevated plasmonic loss at the metal- dielectric interface when the negative permittivity of the metal and the positive permittivity of the dielectric material have matched in their absolute values. The latter breakdown can be avoided by inserting a thin dielectric spacer with a low permittivity between the metal and dielectric. This study suggests important considerations for designing dielectric resonator metasurfaces at the visible frequencies.