It's a bad idea to hold back a child in any grade. Especially when it is a child with some form of LD. Here are some of the reasons why. Perhaps the 2 most important ones:
1. It seems to him like he is trying himself into the ground. He probably can not try any harder than he already is. So, you are penalizing him for doing his best by not letting him travel on with his peers. You are humiliating him.
2. What does putting him through the same nonsense he already did poorly in actually accomplish if he is getting the exact same delivery a second time around taught in the exact same way? Obviously if he didn't get it in the way it was provided to him the first time round it stands to reason the second time round with the same methodology is not likely to get you anywhere at all.
3. For students with LD school in itself is usually a form of torture pretty much equal in horribleness to being waterboarded. Putting him through that for an extra year is not going to please him. It is not going to acheive any goals at all. It is only going to hurt him more.
However, If they can cater to his learning style and provide an alternative method of getting him the information he needs to know next time around, staying back could be hugely beneficial. But if they don't have a pretty long list of things they will do differently with him this time to meet his learning needs if it were my kid, I would look for teachers less trained in Jesus loves me and more trained in providing information to students with LD. Not all teachers are qualified or even know how to teach to LD students. So find out if his teacher is. Find out how they will do it differently before you decide what to do.
But if it were my kid, well it would never be my kid. Because i would cut my own head off and eat it before a child of mine ever attended a religious school that likely teaches them that evolution is a lie. But that is just me, but if it were my kid, I would not hold them back in the same school. I would look for an alternative program specifically geared towards meeting his LD needs.