During Notch (N)-mediated binary cell fate decisions, cells adopt two different fates according to the levels of N pathway activation: an N-off-dependent or an Non-dependent fate. How cells maintain these N activity levels over time remains largely unknown. We address this question in the cell lineage that gives rise to the Drosophila mechanosensory organs. In this lineage a primary precursor cell undergoes a stereotyped sequence of oriented asymmetric cell divisions and transits through two neural precursor states before acquiring a neuron identity. Using a combination of genetic and cell biology strategies, we show that Escargot and Scratch, two transcription factors belonging to the Snail superfamily, maintain N-off neural commitment by directly blocking the transcription of N target genes. We propose that Snail factors act by displacing proneural transcription activators from DNA binding sites. As such, Snail factors maintain the Noff state in neural precursor cells by buffering any ectopic variation in the level of N activity. Since Escargot and Scratch orthologs are present in other precursor cells, our findings are fundamental for understanding precursor cell fate acquisition in other systems.