Just as every dog won't be a good match for your family, neither will every rescue. Rescues don't all have the same views when it comes to placing dogs. Some, especially the rescues that don't take in huge numbers of dogs, tend to be most selective when it comes to placing dogs. Some have black and white policies and don't make exceptions.
My sister wanted to adopt a golden retriever, but had a daughter under the age of seven and the GR rescue denied her adoption application. They didn't even talk to her or any of her references. Nor did it seem to matter that she owned a golden who died due to cancer, so was very familiar with the breed. They denied her flat out.
Have you checked for rescues or available dogs on
www.Petfinder.com? Check out these cuties:
Petfinder Adoptable Dog | Havanese | Kent, OH | Sarah Petfinder Adoptable Dog | Maltese | Kent, OH | Frankie Petfinder Adoptable Dog | Schnauzer | Kent, OH | Sparkle Petfinder Adoptable Dog | Havanese | Kent, OH | Jasper Petfinder Adoptable Dog | Cairn Terrier | Medina, OH | Broderick in IL Petfinder Adoptable Dog | Poodle | Warren, OH | Mitzy
There were many more. Good luck with your search.