Parents have their own religious beliefs, but their children may not abide by the same beliefs (and in many cases where they do, it is often the result of religious indoctrination). A parent should not have the right to force a child to forgo medical treatment for their own religious reasons.
http://www.sciencebasedmedicine.org/faith-healing-religious-freedom-vs-child-protection/ look up this website. I highly recommend it. It was a well thought out article. Personally, I believe that it should be outlawed. Though yes you have your own religious freedoms, you do not have the right to take away that from your own children. Especially when it is an easily treated illness.
Yes, faith healing of children should be illegal. While an individual has the right to believe and practice any beliefs that s/he wishes, that person's right to those beliefs becomes invalid when those beliefs endanger another person. Faith healing endangers children, therefore, the practice of such healing should be banned.
There's no harm to faith healing as long as medical treatment is also being used. Parents who chose to use ONLY faith healing and let their children suffer and/or die because of it ought to be charged with child abuse, and I'm assuming that's what this question is really asking, even though it's not stated. I know there are some groups who don't use medical treatments and let people die and that's despicable and anyone who does it to a child should be punished. There are some states who allow this sort of thing to go on and that is just ridiculous.
While faith healing sounds like a nice thing it should not be done on children mostly because children are not old enough or mature enough to make such decisions and for a parent to make such a decision on a child's behalf may be infringing on the child's basic human rights.
Decisions like this should be left for the child to make when they're a teenager or an adult.
Touchy question, will surely be a lot of mixed reaction here. It's hard to flat out suggest that something should become law when you're dealing with faith, emotion, and superstition. Ultimately, I think this is largely due to the parents, since a child can't be held accountable for his/her decisions under law until a certain age, and is represented by his parents/guardians. Certainly everyone should have the right to life, and we have more than enough evidence to suggest that this prayer is 100% ineffective. It's completely irrational and sad for all involved. It's nice that the parents are wanting to heal their children, and have good intentions, unfortunately it simply does not work, and needs intervention.
You can not use the same arguments that you would use against not seeking medical treatment based on religious reasons. The question does not stipulate that faith healing is being used in lieu of conventional medical treatment, therefore, there is no basis for making it illegal. While I am not a huge advocate for faith healing, it is my understanding that many seek this course when other options have failed. If this is a part of the parents' religious beliefs and no harm is done to the child why on earth should it be illegal? Should it also be illegal to make a child sit through Sunday school? I believe firmly in the separation of church and state, but it goes both ways.
I've racked my mind, for a negative of faith healing, and cannot find a single one. Faith healing is free, so we can rule out the factor of the church trying to con us. There isn't anybody, forcing us to seek faith healing, its a personal choice, and if someone did have a desire to have faith healing they could too, undergo medial treatment you must remember,there isn't a 'one or the other' rule here. Children have very open minds, and if they find interest in a certain faith, then i think that would be valuable for the child. Faith healers are not trying to subconsciously defraud us, or persuade us to join their faith, however they may give you an insight of their faith to be polite. And my last point, there really isn't a legitimate reason to make it illegal, as there really isn't anything to lose, it either works or it doesn't. You don't give anything in return, and do you pay them, that's the incredible thing about faith, they do it for the common good of everybody. Believe it or not, they are not out to get you, nor are they trying to shove their faith down your throat.