Prognostic is a potential tool for improving the durability of solid oxide fuel cells (SOFCs), which usually involves building a degradation model for prediction. However, the existing degradation models based on parallel constant operation datasets are inaccurate for integration with operation optimization and control problems of SOFCs under varying-load operation due to the nonuniform degradation behaviors. To address this issue, a link function degradation model is proposed, and its parameters are identified online with a cyclic batch identification procedure based on the maximum likelihood method, which provides results representing the degradation trend on a timescale of 10 h. The link function takes the form of an empirical function, which describes how operating parameters affect the degradation and is easy to integrate with control designs. The existence of the link function is proven on the varying-load experiment datasets of two flat-chip SOFCs because it statistically improves the prediction accuracy and stability compared with a constant degradation speed model. Furthermore, the effectiveness of the proposed identification procedure for time-varying degradation behaviors on the timescale of 10 h is also validated with 30,000-h simulation datasets.