The latent reservoir for HIV-1 in resting CD4⁺ T cells is a major barrier to cure. Several lines of evidence suggest that the latent reservoir is maintained through cellular proliferation. Analysis of this proliferative process is complicated by the fact that most infected cells carry defective proviruses. Additional complications are that stimuli that drive T cell proliferation can also induce virus production from latently infected cells and productively infected cells have a short in vivo half-life. In this ex vivo study, we show that latently infected cells containing replication-competent HIV-1 can proliferate in response to T cell receptor agonists or cytokines that are known to induce homeostatic proliferation and that this can occur without virus production. Some cells that have proliferated in response to these stimuli can survive for 7 d while retaining the ability to produce virus. This finding supports the hypothesis that both antigen-driven and cytokine-induced proliferation may contribute to the stability of the latent reservoir. Sequencing of replication-competent proviruses isolated from patients at different time points confirmed the presence of expanded clones and demonstrated that while some clones harboring replication-competent virus persist longitudinally on a scale of years, others wax and wane. A similar pattern is observed in longitudinal sampling of residual viremia in patients. The observed patterns are not consistent with a continuous, cell-autonomous, proliferative process related to the HIV-1 integration site. The fact that the latent reservoir can be maintained, in part, by cellular proliferation without viral reactivation poses challenges to cure.