Rehearsal approaches enjoy immense popularity with Continual Learning (CL) practitioners. These methods collect samples from previously encountered data distributions in a small memory buffer; subsequently, they repeatedly optimize on the latter to prevent catastrophic forgetting. This work draws attention to a hidden pitfall of this widespread practice: repeated optimization on a small pool of data inevitably leads to tight and unstable decision boundaries, which are a major hindrance to generalization. To address this issue, we propose Lipschitz-DrivEn Rehearsal (LiDER), a surrogate objective that induces smoothness in the backbone network by constraining its layer-wise Lipschitz constants w.r.t. replay examples. By means of extensive experiments, we show that applying LiDER delivers a stable performance gain to several state-of-the-art rehearsal CL methods across multiple datasets, both in the presence and absence of pre-training. Through additional ablative experiments, we highlight peculiar aspects of buffer overfitting in CL and better characterize the effect produced by LiDER. Code is available at https://github.com/aimagelab/LiDER.