Visceral leishmaniasis (VL) is a fatal disease and a growing public health problem in East Africa, where Ethiopia has one of the highest VL burdens. The largest focus of VL in Ethiopia is driven by high prevalence in migrant agricultural workers and associated with a high rate of co-infection with HIV. This co-infection makes VL more difficult to treat successfully, and is associated with a high rate of relapse, with VL/HIV patients frequently experiencing many relapses of VL before succumbing to this infection. We present genome-wide data on Leishmania donovani isolates from a longitudinal study of cohorts of VL and VL/HIV patients reporting to a single clinic in Ethiopia. Extensive clinical data allows us to investigate the influence of co-infection and relapse on the populations of parasites infecting these patients. We find that the same parasite population is responsible for both VL and VL/HIV infections, and that in most cases, disease relapse is caused by recrudescence of the population of parasites that caused primary VL. Complex, multi-clonal infections are present in both primary and relapse cases, but the infrapopulation of parasites within a patient loses genetic diversity between primary disease presentation and subsequent relapses, presumably due to a population bottleneck induced by treatment. These data suggest that VL/HIV relapses are not caused by genetically distinct parasite infections, nor by re-infection. Treatment of VL does not lead to sterile cure, and in VL/HIV the infecting parasites are able to re-establish after clinically successful treatment, leading to repeated relapse of VL.