We study the time development of the population of X-type critical points in a two-dimensional magnetohydrodynamic model during the early stages of freely decaying turbulence. At sufficiently high magnetic Reynolds number Rem, we find that the number of neutral points increases as Rem3/2, while the rates of reconnection at the most active sites decrease. The distribution of rates remains approximately exponential. We focus in particular on delicate issues of accuracy, which arise in these numerical experiments, in that the proliferation of X-points is also a feature of under-resolved simulations. The “splitting” of neutral points at high Reynolds number appears to be a fundamental feature of the cascade that has important implications for understanding the relationship between reconnection and turbulence, an issue of considerable importance for the Magnetospheric Multiscale and Solar Probe missions as well as observation of reconnection in the solar wind.