Promoting Life-Saving New Therapies for Neonates Act of 2017 This bill amends the Federal Food, Drug, and Cosmetic Act to require the Food and Drug Administration (FDA) to award the sponsor of a new drug or biological product for the treatment of newborns a neonatal drug exclusivity voucher upon approval of the medication. A neonatal drug exclusivity voucher is a transferable voucher for a one-year extension of all existing patents and marketing exclusivities for a brand name medication. For a sponsor to be eligible for a voucher, the new medication must: (1) treat a condition identified in the Priority List of Critical Needs for Neonates required under this bill, and (2) have been studied in newborns. A voucher may be revoked if the new medication is not marketed in the United States within one year of approval. A voucher may not be used: (1) to extend the marketing exclusivity period for a drug for which the FDA requires an assessment of the safety and effectiveness in newborns, or (2) on the same product as a priority review voucher. A sponsor intending to use a voucher must notify the FDA at least 15 months before the expiration of the patents or exclusivity to be extended. The Government Accountability Office must study the effectiveness of this voucher program.