Prematurity Research Expansion and Education for Mothers who deliver Infants Early Reauthorization Act or PREEMIE Reauthorization Act - Amends the Prematurity Research Expansion and Education for Mothers who deliver Infants Early Act to revise and reauthorize requirements for research on prematurity and preterm births.

Requires the Director of the Office for the Advancement of Telehealth to give preference in awarding grants to an eligible entity that proposes to use the grant funds to develop plans for, or to establish, telehealth networks that provide prenatal care for high-risk pregnancies.

Revises and reauthorizes through FY2017 the authority of the Secretary of Health and Human Services (HHS) to conduct demonstration projects related to preterm births.

Repeals establishment of the Interagency Coordinating Council on Prematurity and Low Birthweight.

Authorizes the Secretary to establish the Advisory Committee on Infant Mortality. Directs the Advisory Committee (or an existing advisory committee designated by the Secretary) to develop, and periodically review and revise, a plan for conducting and supporting research, education, and programs on preterm birth through HHS.

Requires the Secretary to designate an appropriate agency within HHS to coordinate existing studies and report to the Secretary and Congress on hospital readmissions of preterm infants.