There have been studies done since before I became a teacher. And now that I’m retired, I’m talking about decades of research:

Jimerson looked at 20 studies published between 1990 and 1999, and concluded that they “fail to demonstrate that grade retention provides greater benefits to students with academic or adjustment difficulties than does promotion to the next grade.” In many studies, students who were retained had worse academic achievement and social-emotional outcomes than students who were not.

Another research review from Jimerson and his colleagues, this one published in 2002, found that grade retention was also linked strongly to dropping out of high school. -source

The source also brings up the racist underpinnings that too often support holding kids back. I said before, but just to reiterate, there is a problem that needs to be addressed, but retention is demonstrably not the answer.