This article investigates the problem of remote state estimation for nonlinear systems via a fading channel, where the packet losses may occur over the sensor-to-estimator communication network. The risk-sensitive (RS) approach is introduced to formulate the estimation problem with intermittent measurements such that an exponential cost criterion is minimized. Based on the reference measure method, the closed-form expression of the nonlinear RS estimator is derived. Moreover, stability conditions for the designed estimator are established by extending the contraction analysis of the linear cases. In contrast to the linear cases, a novel cost function is designed to obtain the finite-dimensional nonlinear estimate, which counteracts the linearization errors by treating them as model uncertainties. Simulation results illustrate that the proposed nonlinear estimator achieves better estimation qualities compared with the existing nonlinear minimum mean square error methods.