Stem and embryonic cells facilitate programming toward multiple daughter cell fates, whereas differentiated cells resist reprogramming and oncogenic transformation. How alterations in the chromatin-based machinery of epigenetic inheritance contribute to these differences remains poorly known. We observed random, heritable changes in GAL4/UAS transgene programming during Drosophila ovarian follicle stem cell differentiation and used them to measure the stage-specific epigenetic stability of gene programming. The frequency of GAL4/UAS reprogramming declines more than 100-fold over the nine divisions comprising this stem cell lineage. Stabilization acts in cis , suggesting that it is chromatin-based, and correlates with increased S phase length. Our results suggest that stem/early progenitor cells cannot accurately transmit nongenetic information to their progeny; full epigenetic competence is acquired only gradually during early differentiation. Modulating epigenetic inheritance may be a critical process controlling transitions between the pleuripotent and differentiated states.