I don't know what the actual term is for what I'm referring to, but "Temporary Partial Student Retention" is the best name that I can think dubbing it with. This hasn't actually happened yet, but I have heard it discussed between Mr. Agajan (a 3rd grade teacher) and a 4th grade teacher. It turns out that this 4th grade teacher has a student who is doing fine with all the other subjects in 4th grade, but is doing poorly in math.
In that case, it doesn't make sense to completely require him to take 3rd grade again does it? I say that it doesn't make sense. However, she has decided that she wants to send this student to Mr. Agajan's 3rd grade class to brush up on his math skills. Since he would only stay in Mr. Agajan's class to brush up his math skills, his retention in 3rd grade is only partial.
This 4th grade student would brush up on his math skills with Mr. Agajan (whether in private or as apart of a class) for as long as it takes him to master them to the necessary extent. Presumably, some of 3rd grade math is familiar to this 4th grade student. In which case, this student will not need a full school year to master the 3rd grade math which he needs for 4th grade. That the 4th grade student's presence in Mr. Agajan's class would be temporary is based on that presumption.
That's my understanding of how and why a "temporary partial student retention" would occur.