One study found that holding kids back at third grade when they don't meet the academic standards will give them a boost in achievement, by some measures. The researchers found large positive effects on achievement that fade out entirely when retained students are compared to their same-age peers, but remain substantial through grade 10 when compared to students in the same grade. Being retained in third grade due to missing the promotion standard increases students' grade point averages and leads them to take fewer remedial courses in high school but has no effect on their probability of graduating.
Schwerdt, G., West, M. R., & Winters, M. A. (2017). The effects of test-based retention on student outcomes over time: Regression discontinuity evidence from Florida. Journal of Public Economics, 152, 154-169. https://dx.doi.org/10.1016/j.jpubeco.2017.06.004.