This paper addresses fault-tolerant control for position mooring of a shuttle or floating production storage and offloading vessels. A complete framework for fault diagnosis is presented. A loss of a sub-sea mooring line buoyancy element and line breakage are given particular attention, since such failures might cause high-risk abortion of an oil-loading operation. With significant drift forces from waves, non-Gaussian elements dominate forces and the residuals designed for fault diagnosis. Hypothesis testing is designed using dedicated change detection for the type of distribution encountered. A new position recovery algorithm is proposed as a means of fault accommodation in order to keep the mooring system in a safe state, despite faults. The position control is shown to be capable of accommodating serious failures and preventing breakage of a mooring line, or a loss of a buoyancy element, from causing subsequent failures. Properties of the detection and fault-tolerant control algorithms are demonstrated by high fidelity simulations.