What happens if a temporary care and custody agreement isn't renewed and the society won't agree to return the child?

If a temporary care and custody agreement isn't renewed and reaches its end, the society's authority to keep the child in its care under that agreement ends with it - the society doesn't get to simply continue holding the child informally because it disagrees with returning them. If the society still believes the child needs protection at that point, its proper route is to apply to the child protection court for its own order, rather than refusing to return the child without a court's involvement.

If you're in this situation, put your request for the child's return in writing, and ask the society directly and promptly what its position is and whether it intends to bring a court application. If the society refuses to return the child and hasn't started a court process, that's a serious issue worth raising with a lawyer immediately, since it goes to whether the society is acting within its actual legal authority. Where the society does bring an application, you'll have the opportunity to respond to it in court, with legal representation, rather than the decision being made outside the court process.