Group A Streptococcus (GAS) skin infections are caused by a diverse array of strain types and are highly prevalent in disadvantaged populations. The role of strain-specific immunity in preventing GAS infections is poorly understood, representing a critical knowledge gap in vaccine development. A recent GAS murine challenge study showed evidence that sterilising strain-specific and enduring immunity required two skin infections by the same GAS strain within three weeks. This mechanism of developing enduring immunity may be a significant impediment to the accumulation of immunity in populations. We used an agent-based mathematical model of GAS transmission to investigate the epidemiological consequences of enduring strain-specific immunity developing only after two infections with the same strain within a specified interval. Accounting for uncertainty when correlating murine timeframes to humans, we varied this maximum inter-infection interval from 3 to 420 weeks to assess its impact on prevalence and strain diversity, and considered additional scenarios where no maximum inter-infection interval was specified. Model outputs were compared with longitudinal GAS surveillance observations from northern Australia, a region with endemic infection. We also assessed the likely impact of a targeted strain-specific multivalent vaccine in this context. Our model produced patterns of transmission consistent with observations when the maximum inter-infection interval for developing enduring immunity was 19 weeks. Our vaccine analysis suggests that the leading multivalent GAS vaccine may have limited impact on the prevalence of GAS in populations in northern Australia if strain-specific immunity requires repeated episodes of infection. Our results suggest that observed GAS epidemiology from disease endemic settings is consistent with enduring strain-specific immunity being dependent on repeated infections with the same strain, and provide additional motivation for relevant human studies to confirm the human immune response to GAS skin infection.