Here is some more information about blue born from
Health Issues :
"The Yorkshire Terrier is genetically a Black/Tan (B/T) dog that turns blue later in life. The blue color is created at another loci by the GG or Gg genes. Whenever you have a dog born one color that turns blue later in life, it is the GG or Gg genes that cause this to happen.
When a dog is born blue it is different genes that effects that then the GG genes. The dd gene is what causes this at birth and the Yorkshire Terrier should only be carrying the DD. A blue born puppy will also have self colored pigment, such as blue nose. The DD gene is what allows them to be born Black/Tan. The upper case always means dominant and the lower case always means recessive. This is obviously a deep buried recessive that the animals are carrying that they have passed onto the resulting puppies. The breeds that are born blue are born with the dd gene, but in Yorkshire Terriers this should not be the situation to cause the blue coloring.
Unfortunately with blue born puppies the situation is usually fatal. Very few live beyond the 1st few days. The ones that do survive almost always at the time they would normally break blue, lose all their blue body coat and get a very leathery skin that is like an elephant hide and causes the dog to be in extreme pain."
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Just my opinion now -
...And having the parents also spayed/neutered is just my opinion and what I would do if this happened to me.