Transcriptional memory of gene expression enables adaptation to repeated stimuli across many organisms. However, the regulation and heritability of transcriptional memory in single cells and through divisions remains poorly understood. Here, we combined microfluidics with single-cell live imaging to monitor Saccharomyces cerevisiae galactokinase 1 (GAL1) expression over multiple generations. By applying pedigree analysis, we dissected and quantified the maintenance and inheritance of transcriptional reinduction memory in individual cells through multiple divisions. We systematically screened for loss- and gain-of-memory knockouts to identify memory regulators in thousands of single cells. We identified new loss-of-memory mutants, which affect memory inheritance into progeny. We also unveiled a gain-of-memory mutant, elp6 Delta, and suggest that this new phenotype can be mediated through decreased histone occupancy at the GAL1 promoter. Our work uncovers principles of maintenance and inheritance of gene expression states and their regulators at the single-cell level.