Many countries have made major commitments to carbon sequestration through reforestation under the Paris Climate Agreement, and recent studies have illustrated the potential for large amounts of carbon sequestration in tropical second-growth forests. However, carbon gains in second-growth forests are threatened by non-permanence, i.e. release of carbon into the atmosphere from clearing or disturbance. The benefits of second-growth forests require long-term persistence on the landscape, but estimates of carbon potential rarely consider the spatio-temporal landscape dynamics of second-growth forests. In this study, we used remotely sensed imagery from a landscape in the Peruvian Amazon to examine patterns of second-growth forest regrowth and permanence over 28 years (1985-2013). By 2013, 44% of all forest cover in the study area was second growth and more than 50% of second-growth forest pixels were less than 5 years old. We modeled probabilities of forest regrowth and clearing as a function of landscape factors. The amount of neighboring forest and variables related to pixel position (i.e. distance to edge) were important for predicting both clearing and regrowth. Forest age was the strongest predictor of clearing probability and suggests a threshold response of clearing probability to age. Finally, we simulated future trajectories of carbon sequestration using the parameters from our models. We compared this with the amount of biomass that would accumulate under the assumption of second-growth permanence. Estimates differed by 900,000 tonnes, equivalent to over 80% of Peru's commitment to carbon sequestration through community reforestation under the Paris Agreement. Though the study area has more than 40,000 hectares of second-growth forest, only a small proportion is likely to accumulate significant carbon. Instead, cycles between forest and non-forest are common. Our results illustrate the importance of considering landscape dynamics when assessing the carbon sequestration potential of second-growth forests.