Micro- and nano-resonators have been widely used in force, mass and displacement sensors, surface scanning technologies, and MEMS devices. Understanding the intrinsic dissipation mechanisms that limit the size of the quality factor is important for optimizing nanoscale resonators. Metallic glasses represent a promising class of materials for nanoscale resonators since they are structurally disordered without topological defects, such as dislocations that readily dissipate energy. We describe computational studies to measure the quality factor of thin metallic glass cantilevers subjected to bending vibrations. We show that there is a characteristic amplitude of the vibrations that gives rise to the first atomic rearrangement event, which causes significant loss in the system. Atomic rearrangements cause leakage of energy in a given low frequency mode of vibration to a continuous spectrum of higher frequency modes. We also show that the critical amplitude for the first atomic rearrangement decreases as the size of the cantilever increases, whereas it increases as a function of the cooling rate used to prepare the system. We show that the quality factor of nanoscale resonators can exceed 106 for vibration-induced strains less than 10-4 and cooling rates below 107 K/s.