Continual learning aims to train models that can incrementally acquire new knowledge over a sequence of tasks while retaining previously learned information, even in the absence of access to past data. A key challenge in this setting is maintaining stability at task transitions, where even methods like experience replay can suffer from temporary performance degradation known as the stability gap. In this work, we evaluate Layerwise Proximal Replay (LPR), a recently proposed optimisation strategy that constrains updates at the layer level to preserve internal representations of past data. We implement LPR on a simple multi-layer perceptron and benchmark it against an incremental joint training baseline on a domain-incremental variant of Rotated MNIST. To quantify the stability gap, we track accuracy drops immediately following task switches and compute local minima after transitions. Our results show that LPR consistently reduces the stability gap across a range of learning rates, with statistically significant improvements at higher values. However, this improvement comes at the cost of reduced performance on later tasks. These findings demonstrate that LPR significantly mitigates short-term performance degradation at task boundaries while maintaining high learning rates, offering a practical solution for increased stability in continual learning.