Persistent SARS-CoV-2 infections have been hypothesized to play a key role in the emergence of variants of concern. However, the factors determining which individuals are at risk and their viral molecular signatures during infection remain poorly understood. Using Denmark's extensive COVID-19 surveillance, comprising over 700,000 genomes, we identify 303 persistent infections and, critically, link them to health and sociodemographic data. Our analysis confirms the hypothesis that immunocompromised individuals are at the highest risk of experiencing persistent infections. Other disease groups associated with mortality, such as diabetes, show no such associations. Among these persistent infections, the viral sequences exhibit signs of positive selection, with recurrent mutations linked to treatment resistance. Our findings suggest that immunosuppression plays a key role in the emergence of novelty in persistent infections.