We investigate the role of magnetic helicity in promoting cyclic magnetic activity in a global, 3D, magnetohydrodynamic (MHD) simulation of a convective dynamo. This simulation is characterized by coherent bands of toroidal field that exist within the convection zone, with opposite polarities in the northern and southern hemispheres. Throughout most of the cycle, the magnetic helicity in these bands is negative in the northern hemisphere and positive in the southern hemisphere. However, during the declining phase of each cycle, this hemispheric rule reverses. We attribute this to a global restructuring of the magnetic topology that is induced by the interaction of the bands across the equator. This band interaction appears to be ultimately responsible for, or at least associated with, the decay and subsequent reversal of both the toroidal bands and the polar fields. We briefly discuss the implications of these results within the context of solar observations, which also show some potential evidence for toroidal band interactions and helicity reversals.