The limits on MEMS resonant sensor performance set by nonlinearity are often studied through a model of a Duffing resonator, with linear actuation. This model largely fails to capture the properties of MEMS resonant sensors with electrostatic gap-closing actuation. We have shown that a specific feature of such ubiquitous resonators is that their stability is strongly sensitive to the waveform used to drive them to resonance. In this paper, we conduct an analytical investigation of these phenomena and validate our theoretical results transient simulations.