Can the guardians of a brain damaged adult living in a group home refuse his move to a nursing home if they feel his health will be compromised?

Absolutely !!!!!! You can absolutely refuse consent to transfer the ward if you feel his health with be compromised.  You should call a meeting with the people that run the group home and determine what is the motivation for moving him out.  Do they feel they are no longer able to provide care him?  Has his need for care exceeded what the facility can provide?  You are entitled to all of this information, and entitled to refuse to move him.  Good luck - if I can be of any assistance, please call my office.