© 2018 The Combustion Institute. In turbulent premixed flame propagation, the formation of isolated pockets of reactants or products is associated with flame pinch-off events which cause rapid changes in the flame surface area. Previous topological analysis of these phenomena has been carried out based on Morse theory and Direct Numerical Simulation (DNS) in two spatial dimensions. The present work extends the topological analysis to three dimensions with emphasis on the formation and subsequent burnout of reactant pockets. Singular behaviour observed previously for terms of the Surface Density Function (SDF) transport equation in the two-dimensional case is shown to occur also in three dimensions. Further singular behaviour is observed in the displacement speed close to reactant pocket burnout. The theory is compared against DNS data from hydrogen-air flames and good agreement is obtained.