Centromeres are defined by a self-propagating chromatin structure based on stable inheritance of CENP-A containing nucleosomes. Here, we present a genetic screen coupled to pulse-chase labeling that allow us to identify proteins selectively involved in deposition of nascent CENP-A or in long-term transmission of chromatin-bound CENP-A. These include factors with known roles in DNA replication, repair, chromatin modification, and transcription, revealing a broad set of chromatin regulators that impact on CENP-A dynamics. We further identify the SUMO-protease SENP6 as a key factor, not only controlling CENP-A stability but virtually the entire centromere and kinetochore. Loss of SENP6 results in hyper-SUMOylation of CENP-C and CENP-I but not CENP-A itself. SENP6 activity is required throughout the cell cycle, suggesting that a dynamic SUMO cycle underlies a continuous surveillance of the centromere complex that in turn ensures stable transmission of CENP-A chromatin.