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Crossbars of resistive memories, or memristors, provide a road to reduce the energy consumption of artificial neural networks, by naturally implementing multiply accumulate operations, their most basic calculations. However, a major challenge of implementing robust hardware neural networks is the conductance instability over time of resistive memories, due to the local recombination of oxygen vacancies. This effect causes resistive memory‐based neural networks to rapidly lose accuracy, an issue that is sometimes overlooked. Herein, this conductance instability issue is shown, which can be avoided without changing the material stack of the resistive memory by exploiting an original programming strategy. This technique relies on program‐and‐verify loops with appropriately chosen wait times and ensures that the resistive memories are programmed into states with stable filaments. To test the strategy, a 32 × 32 in‐memory computing system, fabricated in a hybrid complementary metal‐oxide‐semiconductor (CMOS)/hafnium oxide technology, is programmed to classify heart arrhythmia from electrocardiogram. When the resistive memories are programmed conventionally, the system loses accuracy within hours. In contrast, when using this technique, the system maintains an accuracy of 95% over more than 2 months. These results highlight the potential of resistive memory for the implementation of low‐power neural networks with long‐term stability.