I actually had this happen with me when I was a little girl back in the early 80's.  I was rather intelligent as a child, and my issue was that I couldn't stop running my mouth.  I loved to talk.  The teacher tried to get my parents to agree to holding me back a year until I "matured".  

Long story short, it did not happen.  Unless there are serious discipline issues, or behavioral problems, this shouldn't even come up; especially not at the END of the school year.

It's rather interesting how instead of testing a child for higher intelligence, it is automatically assumed that the child is immature.  Think about it, how many "mature" 5 year olds do you know?  

I would fight this decision, of course starting with the principal and then moving as high as you could until someone with common sense gave you the correct information.

Lastly, one thing that helped me was doing more advanced things during the summer, and my parents giving me more responsibilities around our home.  I began to feel important, and in the end started growing a little!

To answer the question simply, yes! In fact, it's probably more common to retain a student for reasons like "maturity" than it is for academic concerns. Typically, it would be an administrative decision - while the teacher may recommend retention, the administration would likely make the actual decision to retain.

Now, this doesn't mean it's a good thing simply because they can. In fact, most research studies suggest that retention is not a good thing. From my experience, retention is rarely a good option, but in some cases can be a positive thing, provided that the repeated grade is actually a new experience - not just a rehash of the same thing. However, unless a child was substantially behind socially or academically, I'd be inclined to not retain a student.

Typically, parents have a substantial amount of say in retention decisions, especially early on, although this depends on the school/district. If you feel that the decision was inappropriate, I'd suggest you schedule a meeting with the appropriate administrator and start getting more information about why that decision was made. Given that it's the start of the school year, I'd do that ASAP as it would be a lot more helpful for the child to start the grade in the right grade, and substantially less likely that a child's placement would be changed once school has started.

If your teacher is speaking to you about holding back your K student-listen!  There is probably no better time than now to be held back, and if all he needs is time to improve, then now is the perfect chance to give it to him.  No, your teacher cannot withhold your child from advancing without your consent, but the fact that your teacher is willing to consider holding back your child (the most expensive and time-consuming plan to improve a child's performance) means she really believes another year will make a difference.  Our son started K at age 4 because he wanted to go to elementary so badly (we lived next to the school) and all his older friends already got to go to there.  He spent his first year in K mostly watching his classmates, (rather than participating) and enjoying recess and story time a lot.  While he met all the criteria to move along to 1st, we fought to have him reattend K, and we're so glad we did!  His second year as a Kinder he "knew" what to do.  Now he was a leader in the classroom (a position he loves to assume!) and eager to show off to the other kids what was expected of them.  He could concentrate and pay attention to the teacher better than his first go-around, and we had the extra time to spend with him.  He did have some problems with a few of his classmates from his first year of K wanting to know why he was still in kinder, (it's a small school, so classrooms are right next to each other) so helping him to have an answer for that was important. We told him it was because he started a year earlier that he needed an extra year of K to catch up with other kids his age, and that the teacher needed a helper for the other kids.  
Let me be clear, we were not worried about him academically-he was already reading, writing and doing higher math before he started kinder.  What he needed was time to learn social skills and develop as a person, and there is NO better time than kindergarten to learn these skills.  We did a lot of research about retention in kindergarten, and we're certain we did the right thing for our son.  Our school made it challenging-we had to attend parenting classes, have both us and our son be psycologically assessed, be willing to work with a tutor to keep him challenged academically, and submit a proposal about why we wished to keep him back, but after complying with all these steps, we're still glad we did it.  We also moved out of the area between 1st and 2nd grade to follow our careers, and now no students at his new school know he attended K twice.  All I can say is follow your instincts, if you really believe your child will not benefit from another year of K, than push for what you believe in.  However, if your teacher really feels repeating K would be beneficial, think through all the pros and cons and try to hear what he/she is saying in a positive light.

I wanted to respond briefly to PSRMom's post: first, congrats on having found the right decision for your child! Sounds like it was a very positive experience, and something that your school took seriously.

My concern would be that most schools do not treat retention in the same way as your school did - most schools would not psychologically assess a child in order to retain him/her, nor assess the parents. In short, it sounds like your school really took the time to examine all of the ramifications of retention for your child, with you doing a lot of research as well. The typical suggestion to retain a child made by most schools is not going to be made with as much assessment, research, planning, and concern, which is why I would caution "infoneeded" from assuming that his/her child's school would be giving as much thought to the situation.

By no means am I intending to take away from your experience - it sounds wonderful! I just wanted to point out that your experience sounds extremely rare in the world of retention, which is unfortunate since it was such a positive and growth-oriented experience for you!

I was held back in kindergarten for this. But it was more of an agreement between my parents and the school. Then I was faced with the same situation with my son. He attended a private kindergarten and we were moving him to a public school. We looked at the scholastic requirements, and even though we felt it was going to be tough due to his immaturity, we felt that he would suffer more from boredom from relearning the same curriculum.  In the end we decided to place him into 1st grade, somewhat against the schools desire. I think that since we discussed it with them and our fears they were more open to moving him forward. He is now in 3rd grade and still in some ways immature for his age but in others he is ahead of his classmates.

I have spoken to some other parents about this and I haven't heard of a school forcing this on parents. My gut tells me that since he passed the test and with "maturity" being a bit subjective they should allow the parents to decide. I think that if your main problem is only the teacher you might involve the Principle in the discussion and that might help. I hope this helps!?!!?