The idea of retaining third graders who can't pass a standardized reading test has its roots in two things: 1) a bunch of research of varying degrees of trustworthiness and usefulness (see here, here, here and here for examples across the scale) and 2) dopey policy makers who don't know the difference between correlation and causation.
What the more reliable research appears to show is that third grade is a good year for taking a student's reading temperature, and their ability to read at the third grade level seems to be a good predictor of future scholastic success. That seems to be a valid correlation but-- say it with me now, nice and loud for the folks in the back-- correlation does not equal causation.
Nevertheless, many states have instituted a plan by which students are not allowed to exit third grade until they can show sufficient reading skills (or at least sufficient standardized read test taking skills). This is dumb.
This would be the equivalent of, say, noting that students who are more than four and a half feet tall in third grade are mostly over six feet tall when they graduate from high school. Therefor, in our desire to make graduates taller, we will not let anyone progress beyond third grade until they are at least four and a half feet tall.
The most likely reading of the third grade reading correlation is that some factors are contributing to a poor reading level, and those same factors, exacerbated by reading difficulties, will be obstacles to future success. Third grade reading level is a canary in the coalmine, and you don't fix things by repeatedly sending canaries down there. But canaries are cheap, and fixing coal mines is hard and expensive. Addressing all the problems that hold a small child back-- well, that's complicated and expensive and difficult and it puts a lot of responsibility on the government. It's simpler to just threaten the kid and the teacher and make it their problem.
Could the results of that test mark certain students for interventions? Yes, but intervention before the test would be ideal (and there are schools that are having some success with this). Hell, intervention before third grade would be ideal. At any rate, telling the kid they've flunked third grade is a blunt instrument, nothing more than a nasty threat to level at an eight year old. Threats only make sense if you believe that teachers and eight year olds are purposefully holding out on education leaders. Yes, I'll bet those six and seven year olds are just laying back, thinking, "I could learn how to read, but I'm not going to bother-- that'll teach those politicians at the state capital a lesson."
It is probably a remarkable coincidence that states have landed on third grade as the year to retain students who fail the standardized test, because that just happens to be the year before students have to take a federally-mandated fourth grade test, the results of which affect school and state standings in education. It's probably a coincidence that retaining third graders who fail a state standardized test keeps them from taking (and failing) the federal high stakes test in fourth grade.
Of course, all of this would be useless quibbling if third grade reading retention worked.
But it doesn't.
Here's just one more study that provides evidence.
The study is from late 2016 and looks at retention in a Florida district, during the 2003-2004 school year. Florida's a great choice because Florida's education leaders have a crazy obsessive love of testing. They once went to court to force a dying, disabled child to take the Big Standardized Test, and they also ended up in court arguing to retain students who had demonstrated reading mastery in umpteen ways-- but who hadn't taken the third grade BS Test.
The results are pretty straightforward. Seven years after retention, 93% remained below proficiency. Similar students who were not retained yielded 85.8% who were not proficient in tenth grade. The district spent $587 million on retention. (there is also some baloney in here about future lost wages which is, in fact, baloney hoping to spark some shiny headlines).
You can dig into the full dissertation by Kathleen Jasper; it's 93 pages long, and it includes, among other things, a thorough review of the mountain of literature that shows that grade retention is almost always a bad thing with a host of bad side-effects for the students who are retained. It's a good resource.
Jasper these days works as the founder/CEO of NavaED, a company that does consulting work in the area of teacher certification and other Floridian bureaucratic hoopjumping. Are they any good? I don't know, but at least Jasper started out her education high muckity muck career with a dissertation that says what many, many sources say and need to keep saying-- third grade reading retention does not work, plus it's expensive and damaging to students, so maybe we can just knock it off right now.