The standard ΛCDM model predicts that the major merger rate of galaxy-size dark matter halos rises rapidly with redshift. The average number of close companions per galaxy, Nc, is often used to infer the galaxy merger rate; however, recent observational studies suggest that Nc evolves very little with redshift. Here we use a ``hybrid'' N-body simulation plus analytic substructure model to predict Nc directly. We identify dark matter subhalos with galaxies and show that the observed lack of close-pair count evolution arises because the high merger rate per halo at early times is counteracted by a decrease in the number of halos massive enough to host a galaxy pair. We compare our results to data compiled from the DEEP2, SSRS2, and UZC redshift surveys. Observed pair counts match our predictions if we assume a monotonic mapping between galaxy luminosity and the maximum circular velocity that each subhalo had when it was first accreted onto its host halo. This suggests that satellite galaxies are significantly more resilient to mass loss than are dissipationless dark matter subhalos. We argue that while Nc does not provide a direct measure of the halo merger rate, it offers a powerful means to constrain both the halo occupation distribution and the spatial distribution of galaxies within halos. Interpreted in this way, close-pair counts provide a useful test of galaxy formation processes on ~10-100 kpc scales.