Transitional Medical Assistance Improvement Act of 2003 - Amends title XIX (Medicaid) of the Social Security Act (SSA) to revise the program commonly referred to as the transitional medical assistance (TMA) program. Authorizes States to: (1) extend the eligibility for TMA of low-income individuals for up to 12 additional months; and (2) allow another six months of eligibility, in certain circumstances, in the case of a family eligible for or receiving Medicaid for less than three of the previous six months. Repeals the sunset date for TMA (thus making the program permanent).