In the field of resonant NEMS design, it is a common misconception that large-amplitude motion, and thus large signal-to-noise ratio, can only be achieved at the risk of oscillator instability. In the present paper, we show that very simple closed-loop control schemes can be used to achieve stable largeamplitude motion of a resonant structure, even when jump resonance (caused by electrostatic softening or Duffing hardening) is present in its frequency response. We focus on the case of a resonant accelerometer sensing cell, consisting in a nonlinear clamped-clamped beam with electrostatic actuation and detection, maintained in an oscillation state with pulses of electrostatic force that are delivered whenever the detected signal (the position of the beam) crosses zero. We show that the proposed feedback scheme ensures the stability of the motion of the beam much beyond the critical Duffing amplitude and that, if the parameters of the beam are correctly chosen, one can achieve almost full-gap travel range without incurring electrostatic pull-in. These results are illustrated and validated with transient simulations of the nonlinear closed-loop system.