Chromosome segregation errors in human oocytes are the leading cause of birth defects, and the risk of aneuploid pregnancy increases dramatically as women age. Accurate segregation demands that sister chromatid cohesion remain intact for decades in human oocytes, and gradual loss of the original cohesive linkages established in fetal oocytes is proposed to be a major cause of age-dependent segregation errors. Here we demonstrate that maintenance of meiotic cohesion in Drosophila oocytes during prophase I requires an active rejuvenation program, and provide mechanistic insight into the molecular events that underlie rejuvenation. Gal4/UAS inducible knockdown of the cohesion establishment factor Eco after meiotic S phase, but before oocyte maturation, causes premature loss of meiotic cohesion, resulting in destabilization of chiasmata and subsequent missegregation of recombinant homologs. Reduction of individual cohesin subunits or the cohesin loader Nipped B during prophase I leads to similar defects. These data indicate that loading of newly synthesized replacement cohesin rings by Nipped B and establishment of new cohesive linkages by the acetyltransferase Eco must occur during prophase I to maintain cohesion in oocytes. Moreover, we show that rejuvenation of meiotic cohesion does not depend on the programmed induction of meiotic double strand breaks that occurs during early prophase I, and is therefore mechanistically distinct from the DNA damage cohesion re-establishment pathway identified in G2 vegetative yeast cells. Our work provides the first evidence that new cohesive linkages are established in Drosophila oocytes after meiotic S phase, and that these are required for accurate chromosome segregation. If such a pathway also operates in human oocytes, meiotic cohesion defects may become pronounced in a woman's thirties, not because the original cohesive linkages finally give out, but because the rejuvenation program can no longer supply new cohesive linkages at the same rate at which they are lost.