Recommender systems have become an integral part of online platforms. Every day the volume of training data is expanding and the number of user interactions is constantly increasing. The exploration of larger and more expressive models has become a necessary pursuit to improve user experience. However, this progression carries with it an increased computational burden. In commercial settings, once a recommendation system model has been trained and deployed it typically needs to be updated frequently as new client data arrive. Cumulatively, the mounting volume of data is guaranteed to eventually make full batch retraining of the model from scratch computationally infeasible. Naively fine-tuning solely on the new data runs into the well-documented problem of catastrophic forgetting. Despite the fact that negative sampling is a crucial part of training with implicit feedback, no specialized technique exists that is tailored to the incremental learning framework. In this work, we propose a personalized negative reservoir strategy, which is used to obtain negative samples for the standard triplet loss of graph-based recommendation systems. Our technique balances alleviation of forgetting with plasticity by encouraging the model to remember stable user preferences and selectively forget when user interests change. We derive the mathematical formulation of a negative sampler to populate and update the reservoir. We integrate our design in three SOTA and commonly used incremental recommendation models. We show that these concrete realizations of our negative reservoir framework achieve state-of-the-art results for standard benchmarks using multiple top-k evaluation metrics.