Explaining the maintenance of tropical forest diversity under the countervailing forces of drift and competition poses a major challenge to ecological theory. Janzen-Connell effects, in which host-specific natural enemies restrict the recruitment of juveniles near conspecific adults, provide a potential mechanism. Janzen-Connell is strongly supported empirically, but existing theory does not address the stable coexistence of hundreds of species. Here we use high-performance computing and analytical models to demonstrate that tropical forest diversity can be maintained nearly indefinitely in a prolonged state of transient dynamics due to distance-responsive natural enemies. Further, we show that Janzen-Connell effects lead to community regulation of diversity by imposing a diversity-dependent cost to commonness and benefit to rarity. The resulting species-area and rank-abundance relationships are consistent with empirical results. Diversity maintenance over long time spans does not require dispersal from an external metacommunity, speciation, or resource niche partitioning, only a small zone around conspecific adults in which saplings fail to recruit. We conclude that the Janzen-Connell mechanism can explain the maintenance of tropical tree diversity while not precluding the operation of other niche-based mechanisms such as resource partitioning.