Re-applying after an educational rejection is a considerable but understated part of access to selective educational institutions. We study social inequalities in stopping applying to university after an educational rejection to identify the extent to which educational intentions are more constrained among students from the lower social strata. We explore applications to universities in Finland, where student selection takes place at the gates of the institutions and in which around two-thirds of the applicants are rejected on their first attempt. With full population register data and discrete-time event-history models, we show that around 40% of rejected applicants stop applying to university each year with substantial social origin differences. Previous national examination grades and various life-course changes after the rejection, such as entering the labor market and having children, account for the social origin gap in stopping applying only partially. We argue that the socially selective queue, in which all students do not have the same incentives or possibilities to stand waiting, reinforces social inequalities in university admissions.