Drawing on a series of sixteen focus groups with Brazilian and Argentine citizens from low-income groups in four cities, this chapter documents the challenges individuals face when trying to access public health and early childhood education benefits. The chapter provides a conceptual framework for classifying citizen responses to these challenges. It argues that while some citizens exit from seeking access to public services, an important response is what the authors call "state-centric persistence": the act of repeatedly and directly engaging with government offices or officials after an initial failed attempt. The focus group narratives illustrate that this form of persistence is often necessary for successful access and that it is distinct from other options like giving up or turning to private alternatives. The chapter also uses survey data to show widespread belief in the usefulness of state-centric persistence.