Social network analysis has become increasingly used to investigate the consequences of individuals’ social tendencies in recent years; however, the question of whether individuals are consistent in their social network position over time or situations has received comparatively scant attention. Knowledge of the degree to which individuals are stable in their social behavior can improve our understanding the fitness consequences of processes such as the transmission of disease and social information through networks, as well as the evolution of social behavior and social structure in general. Here, I investigated individual consistency in social behavior in wild vervet monkeys (Chlorocebus pygerthrus) residing in a highly seasonal habitat. I constructed grooming networks for three time periods characterized by diverse environmental conditions and explored the repeatability of seven network metrics as well as the effects of sex and dominance rank on these metrics. Both female and male vervets were highly consistent in three correlated, weighted measures of social connectedness—grooming in-strength, out-strength, and eigenvector centrality, and in-degree was moderately repeatable in both sexes. In contrast, only males were consistent in their out-degree and clustering coefficient, and there was no evidence of consistency in betweenness for either sex. High-ranking females had higher in-degree and in-strength scores, and high-ranking males had lower out-degree and out-strength, but controlling for dominance rank did not affect the findings regarding the repeatability of any metric. These results add to the small number of studies that have explored the temporal and situational stability of social network phenotypes in wild animals. Relatively few animal social network studies have examined whether individuals are consistent in the positions that they occupy within networks. Determining the degree to which individuals are consistent in their social network characteristics over time and across naturally changing conditions is necessary for a better understanding of the ecology and evolution of social behavior. In this study, I examined individual consistency in several components of social network position in vervet monkeys residing in a highly seasonal environment. I also evaluated the effects of sex and dominance rank on these measures of sociality. I found that both male and female vervets were consistent in most measures of direct connectedness in grooming networks across seasons, but metrics capturing indirect social connections were overall less repeatable. Controlling for the effects of dominance rank on sociality measures did not change these results.