Heat exchanger networks subject to fouling are an important example of dynamic systems where performance deteriorates over time. To mitigate fouling and recover performance, cleanings of the exchangers are scheduled and control actions applied. Because of inaccuracy in the models, as well as uncertainty and variability in the operations, both schedule and controls often have to be revised to improve operations or just to ensure feasibility. A closed-loop nonlinear model predictive control (NMPC) approach had been previously developed to simultaneously optimize the cleaning schedule and the flow distribution for refinery preheat trains under fouling, considering their variability. However, the closed-loop scheduling stability of the scheme has not been analyzed. For practical closed-loop (online) scheduling applications, a balance is usually desired between reactivity (ensuring a rapid response to changes in conditions) and stability (avoiding too many large or frequent schedule changes). In this paper, metrics to quantify closed-loop scheduling stability (e.g., changes in task allocation or starting time) are developed and then included in the online optimization procedure. Three alternative formulations to directly include stability considerations in the closed-loop optimization are proposed and applied to two case studies, an illustrative one and an industrial one based on a refinery preheat train. Results demonstrate the applicability of the stability metrics developed and the ability of the closed-loop optimization to exploit trade-offs between stability and performance. For the heat exchanger networks under fouling considered, it is shown that the approach proposed can improve closed-loop schedule stability without significantly compromising the operating cost. The approach presented offers the blueprint for a more general application to closed-loop, model-based optimization of scheduling and control in other processes.