Community-Based Health Care Retraining Act - Amends the Workforce Investment Act of 1998 to require the Secretary of Labor to establish and carry out a health professions training demonstration project that awards grants to eligible entities to train certain unemployed workers from the manufacturing or service sector for employment as health care professionals in communities with manufacturing and service sector job loss, health professional shortages, or health services shortages, or those designated as a medically underserved community.