Approximate nearest neighbor (ANN) search on high-dimensional vector data is core functionality in an increasing number of real-world applications. However, most existing methods only focus on accelerating search by means of indexing that assumes that the data is static. The few methods capable of contending with dynamic data often face challenges such as decreased query accuracy following updates and low update efficiency. In this study, we propose Wolverine, the first proposal that, to our knowledge, enables efficient monotonic search path repair, thereby solving the graph-based ANN index update problem. Wolverine repairs disrupted monotonic search paths by adding in-edges to the out-neighbors of a point to be deleted. To improve efficiency, Wolverine+ restricts the search space to be within the 2-hop neighbors of the point to be deleted. In addition, Wolverine++ employs a sophisticated candidate selection policy to find high-quality candidates in the reduced search space, simultaneously improving accuracy and efficiency. An experimental study on 9 real-world datasets demonstrates that Wolverine is capable of accelerating the deletion throughput by up to 11X and achieving more stable recall during updates compared to the state-of-the-art dynamic ANN search method.