Numerical instability resulting from coupling isotopic depletion and neutronics is widely reported, but little work has been done to interrogate the phenomenon theoretically. This work extends the pioneering analysis developed by Densmore et al., who examined the stability of a monoenergetic neutron diffusion problem coupled with a simple depletion system through the explicit Euler scheme. Their Fourier stability analysis is applied to the predictor-corrector scheme and its iterated and implicit variants. The results reproduce behaviour described in previous reports of numerical instability and its solution, and develop a future avenue for diagnosing the stability of burn-up problems.