Existing neural solvers for vehicle routing problems (VRPs) are typically trained either in a one-off manner on a fixed set of pre-defined tasks or in a lifelong manner with tasks arriving sequentially, assuming sufficient training on each task. Both settings overlook a common real-world property: problem patterns may drift continually over time, yielding massive tasks sequentially arising, each with only limited training resources. In this paper, we propose a novel lifelong learning paradigm for neural VRP solvers under continual task drift over time, where each task is locally stationary at one learning time step but receives only insufficient training resources. We empirically demonstrate that such continual drift arises in practice using a real-world logistics dataset. We then propose Dual Replay with Experience Enhancement (DREE), a general framework to improve learning efficiency and mitigate catastrophic forgetting under such drift. Extensive experiments based on both the real-world logistics dataset and commonly used synthetic dataset show that, under such continual drift, DREE effectively learns new tasks, preserves prior knowledge, improves generalization to unseen tasks, and can be applied to various existing neural solvers.