Treatment strategies that anticipate and respond to the evolution of pathogens are promising tools for combating the global rise of antibiotic resistance. Mutations conferring resistance to one drug can confer positive or negative cross-resistance to other drugs. The sequential use of drugs exhibiting negative cross-resistance has been proposed to prevent or slow down the evolution of resistance, although factors affecting its efficacy have not been investigated. Here we show that population diversity can disrupt the efficacy of negative cross-resistance-based therapies. By testing 3317 resistant Staphylococcus aureus mutants against multiple antibiotics, we show that first-step mutants exhibit diverse cross-resistance profiles: even when the majority of mutants show negative cross-resistance, rare positive cross-resistant mutants can appear. Using a drug pair showing reciprocal negative cross-resistance, we found that selection for resistance to the first drug in small populations can decrease resistance to the second drug, but identical selection conditions in large populations can increases resistance to the second drug through the appearance of rare positive cross-resistant mutants. We further find that, even with small populations and strong bottlenecks, resistance to both drugs can increase through sequential steps of negative cross-resistance cycling. Thus, low diversity is necessary but not sufficient for effective cycling therapies. While evolutionary interventions are promising tools for controlling antibiotic resistance, they can be sensitive to population diversity and the accessibility of evolutionary paths, and so must be carefully designed to avoid harmful outcomes.