Living: This is not something you decide because of research. This is a personal decision parents make based on the current state of their child. If a child is socially or emotionally underdeveloped compared to their peers, or if other developmental factors are present, then there is nothing wrong with parents holding their children back. I, too, have a "redshirt" in my house, and it was the best decision we could have made for our child.
Fresh: Everyone keeps referring to "maturity" as a reason to hold children back. However, no one seems to be asking, "Is there a reason the child is not 'mature' enough to enter kindergarten?" I fully agree that parents know their children best; however, most parents are not developmental psychologists. My cousin learned this lesson the hard way. She held back her "immature" 5-year-old because she felt he wasn't ready. When he finally went through kindergarten testing (including hearing and vision), it was discovered that he has a degenerative vision issue and is going blind. She doesn't regret holding him back, but she does regret not trying to figure out "why." He lost an entire year of intervention for his vision issues.