The sterile insect technique (SIT) is an appealing method for managing mosquito populations while avoiding the environmental and social costs associated with more traditional control strategies like insecticide application. Success of SIT, however, hinges on sterile males being able to compete for females. As a result, heavy and/or continued use of SIT could potentially diminish its efficacy if prolonged treatments result in selection for female preference against sterile males. In this paper we extend a general differential equation model of mosquito dynamics to consider the role of female choosiness in determining the long-term usefulness of SIT as a management option. We then apply optimal control theory to our model and show how natural selection for female choosiness fundamentally alters management strategies. Our study calls into question the benefits associated with developing SIT as a management strategy, and suggests that effort should be spent studying female mate choice in order to determine its relative importance and how likely it is to impact SIT treatment goals.