Pipe conveyors provide sustainable solutions for environmentally sensitive or topographically complex powdered and bulk-solid handling processes; however, belt rotation is among the most critical failure modes of these equipment, influencing engineering, operational, and maintenance activities throughout the conveyors’ lifecycles. Position changes in the overlap are mechanical responses to uneven contact forces between the vulcanizing rubber belt and the idler rolls, owing to the highly nonlinear process of the belt folding from a trough to a tubular shape, and no method for quantifying the belt’s stability is currently available. In this study, we analyzed the failure mode of belt rotation and proposed a linearized model of an overlap stability index to evaluate the resilience of the overlap position through a case study of a short-flight curved pipe conveyor. Our proposal considers an interference model between the simulated torque of a curved flight in a pipe conveyor and the calculated torque of its equivalent straight flight by using kernel-smoothed density functions. It is adapted to incorporate adjustment factors for the filling degree based on simulations, the effect of the overlap in the forming force of the belt, the remaining useful life of the belt, and the coefficients of friction between the belt back cover and the idler rolls due to adhesion and hysteresis. An application was developed to calculate the belt’s rotational holding torque and rotary moment by processing real operational data, simulated contact forces, and the relevant equipment parameters. This analysis identified the reduced transverse bending stiffness and increased belt tension forces as the root causes for position changes with a loss of contact in the upper idler rolls of curved flights 10, 13, 15–16, and 17. The contributing factors included spots of augmented contact forces during the initial stages of the belt lifespan in curved flights 15–16, which presented unstable conditions due to increased opening forces, with an OSI of 0.8657. Furthermore, we proposed corrective and preventive action plans, an optimized replacement interval for the belt, and recommendations for design changes according to the relevant standards.