Abstract Despite decades of research, the primary factors determining savanna structure remain elusive – a conundrum termed ‘the savanna problem’. After 47 years of annual burning in Terminalia woodland and Acacia/Combretum savanna on sandy, granite-derived soils in the southern Kruger National Park, South Africa, a dense cover of trees and shrubs persists on some burnt plots and is largely absent from others. We postulated that intense browsing pressure by antelope and other herbivores prevents recruitment of trees in burnt plots and that herbivores concentrate on plots that are richest in nutrients. Herbivore abundance did not show a relationship with soil macronutrients and we consequently investigated micronutrient status. The reduction in tree cover as a result of annual burning was positively correlated with mass of herbivores (15–1500 kg) (r 2 = 0.61, n = 8). This index of herbivore abundance was in turn positively correlated with total Zn (r 2 = 0.64, n = 8). Other indices of herbivore abundance showed significant relationships with total clay content and total Mn. We suggest that herbivores concentrate on sites with greater clay content (possibly due to a greater availability of micronutrients), and that tree cover can remain relatively dense under a regime of annual burning if browsing pressure is not intense. The long-term burn experiments in the Kruger National Park savanna provide a platform for unravelling the savanna problem. Determining possible interactions between soil properties, herbivory and fire is a step in this direction.