The problem of control of nonlinear process systems subject to input constraints and sensor faults (complete failure or intermittent unavailability of measurements) is considered. A fault-tolerant controller is designed that utilizes reconfiguration (switching to an alternate control configuration) in a way that accounts for the process nonlinearity, the presence of constraints and the occurrence of sensor faults. To clearly illustrate the importance of accounting, for the presence of input constraints, first the problem of sensor faults that necessitate sensor recovery to maintain closed-loop stability is considered. We address the problem of determining, based on stability region characterizations for the candidate control configurations, which control configuration should be activated (reactivating the primary control configuration may not preserve stability) after the sensor is rectified. We then consider the problem of asynchronous measurements, that is of intermittent unavailability of measurements. To address this problem, the stability region (that is, the set of initial conditions starting from where closed-loop stabilization under continuous availability of measurements is guaranteed), as well as the maximum allowable data loss rate which preserves closed-loop stability for the primary and the candidate backup configurations are computed. This characterization is utilized in identifying the occurrence of a destabilizing sensor fault, and in activating a suitable backup configuration that preserves closed-loop stability. The proposed method is illustrated using a chemical process example and demonstrated via application to a polyethylene reactor.