Centromeres provide a robust model for epigenetic inheritance as they are specified by sequence-independent mechanisms involving the histone H3-variant centromere protein A (CENP-A). Prevailing models indicate that the high intrinsic stability of CENP-A nucleosomes maintains centromere identity indefinitely. Here, we demonstrate that CENP-A is not stable at centromeres but is instead gradually and continuously incorporated in quiescent cells including G0-arrested tissue culture cells and prophase I-arrested oocytes. Quiescent CENP-A incorporation involves the canonical CENP-A deposition machinery but displays distinct requirements from cell cycle-dependent deposition. We demonstrate that Plk1 is required specifically for G1 CENP-A deposition, whereas transcription promotes CENP-A incorporation in quiescent oocytes. Preventing CENP-A deposition during quiescence results in significantly reduced CENP-A levels and perturbs chromosome segregation following the resumption of cell division. In contrast to quiescent cells, terminally differentiated cells fail to maintain CENP-A levels. Our work reveals that quiescent cells actively maintain centromere identity providing an indicator of proliferative potential.