Centromeres are unique chromosomal loci that form the anchorage point for the mitotic spindle during mitosis and meiosis. Their position and function are specified by a unique chromatin domain featuring the histone H3 variant CENP-A. While typically formed on centromeric satellite arrays, CENP-A nucleosomes are maintained and assembled by a strong self-templated feedback mechanism that can propagate centromeres even at non-canonical sites. Central to the epigenetic chromatin-based transmission of centromeres is the stable inheritance of CENP-A nucleosomes. While long-lived at centromeres, CENP-A can turn over rapidly at non-centromeric sites and even erode from centromeres in non-dividing cells. Recently, SUMO modification of the centromere complex has come to the forefront as a mediator of centromere complex stability, including CENP-A chromatin. We review evidence from different models and discuss the emerging view that limited SUMOylation appears to play a constructive role in centromere complex formation, while polySUMOylation drives complex turnover. The deSUMOylase SENP6/Ulp2 and the proteins segregase p97/Cdc48 constitute the dominant opposing forces that balance CENP-A chromatin stability. This balance may be key to ensuring proper kinetochore strength at the centromere while preventing ectopic centromere formation.