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An Independent View of Social Security
Please contact the SSA regarding this, but I see no requirement for obtaining a Social Security number for a deceased newborn. The SSA itself states, "The main reason you should get a Social Security number is to claim your baby as a dependent on your income tax return."
So this is more of an admonition than a requirement.
Also, please see the following from IRS Publication 501 for 2011 returns :
If your child was born and died in 2011, and you do not have an SSN for the child, you may attach a copy of the child’s birth certificate, death certificate, or hospital records instead. The document must show the child was born alive. If you do this, enter "DIED" in column (2) of line 6c of your Form 1040 or Form 1040A.