Visual Place Recognition (VPR) plays a critical role in many localization and mapping pipelines. It consists of retrieving the closest sample to a query image, in a certain embedding space, from a database of geotagged references. The image embedding is learned to effectively describe a place despite variations in visual appearance, viewpoint, and geometric changes. In this work, we formulate how limitations in the Geographic Distance Sensitivity of current VPR embeddings result in a high probability of incorrectly sorting the top-k retrievals, negatively impacting the recall. In order to address this issue in single-stage VPR, we propose a novel mining strategy, CliqueMining, that selects positive and negative examples by sampling cliques from a graph of visually similar images. Our approach boosts the sensitivity of VPR embeddings at small distance ranges, significantly improving the state of the art on relevant benchmarks. In particular, we raise recall@1 from 75% to 82% in MSLS Challenge, and from 76% to 90% in Nordland. Our models and code will be released upon acceptance and are provided as supplemental material.