Robust chaos in a dynamical system is characterized by the persistence of the chaotic attractor with changes in the system parameters and is generally required in practical applications based upon physical sources of chaos. However, for applications that rely upon continuous time chaotic signals, there are now very few alternatives of dynamical systems with robust chaos that could be used. In this context, it is important to find a new dynamical system and, particularly, new physical systems that present robust chaos. In this work, we show through simulations that a relevant physical system, suspended beam micro and nanoelectromechanical resonators, can present robust chaos when excited by two distinct frequencies. To demonstrate the existence of robust chaos in the system, we perform an extensive numerical analysis, showing that the attractor is unique and changes smoothly in a large region of the relevant physical parameter space. We find that the robustness of the chaotic dynamics depends crucially on the dissipation, which must be sufficiently small. When the dissipation is small, we find a large range of frequencies, frequency ratios, and applied voltages where robust chaos is observed. These findings turn these systems into viable and strong candidates for practical applications since the chaotic dynamics becomes quite insensitive to fabrication tolerances, changes in the physical parameters induced by the environment, and aging.