In this paper, we present a fault-tolerant control scheme for linear parameter-varying systems that utilises multiple sensor switching to compensate for sensor faults. The closed-loop scheme consists of an estimator-based feedback tracking controller and sensor-estimate switching strategy which allows for the reintegration of previously faulty sensors. The switching mechanism tracks the transitions from faulty to healthy behaviour by means of set separation and pre-computed transition times. The sensor-estimate pairings are then reconfigured based on available healthy sensors. Under the proposed scheme, preservation of closed-loop system boundedness is guaranteed for a wide range of sensor fault situations. An example is presented to illustrate the performance of the fault-tolerant control strategy.