In emerging multi-robot societies, heterogeneous agents must continually extract and integrate local knowledge from one another through communication, even when their internal models are completely opaque. Existing approaches to continual or collaborative learning for visual place recognition (VPR) largely assume white-box access to model parameters or shared training datasets, which is unrealistic when robots encounter unknown peers in the wild. This paper introduces \emph{Continual Communicative Learning (CCL)}, a data-free multi-robot framework in which a traveler robot (student) continually improves its VPR capability by communicating with black-box teacher models via a constrained query--response channel. We repurpose Membership Inference Attacks (MIA), originally developed as privacy attacks on machine learning models, as a constructive communication primitive to reconstruct pseudo-training sets from black-box VPR teachers without accessing their parameters or raw data. To overcome the intrinsic communication bottleneck caused by the low sampling efficiency of black-box MIA, we propose a prior-based query strategy that leverages the student's own VPR prior to focus queries on informative regions of the embedding space, thereby reducing the knowledge transfer (KT) cost. Experimental results on a standard multi-session VPR benchmark demonstrate that the proposed CCL framework yields substantial performance gains for low-performing robots under modest communication budgets, highlighting CCL as a promising building block for scalable and fault-tolerant multi-robot systems. Furthermore, we propose a Distributed Statistic Integration (DSI) framework that theoretically eliminates catastrophic forgetting by efficiently aggregating sufficient statistics from black-box VPR models while maintaining data privacy and reducing communication overhead to a sample-invariant constant complexity.