Summary We investigate household electricity access in a poor rural setting in South Africa, showing that the acquisition of connections is not the simple monotonic process often assumed in the literature. We argue that changes in household electricity access are a complex and changing outcome of two key time-varying processes: (1) net connections (new connections less disconnections) and (2) household formation and dissolution dynamics. In particular, we show that migration can occur in ways which either improves or worsens access. Even for households that stay in place we observe many disconnections. Therefore, in their efforts to improve access to electricity, governments in developing countries may in fact be aiming for a moving target—if the infrastructure is provided in places from which people are migrating, if many new households are being formed in un-serviced areas, or if existing connections are being lost.