**Core Concept**
A duct-dependent lesion refers to a congenital heart defect that relies on the patency of the ductus arteriosus for survival. The ductus arteriosus is a vital fetal shunt that connects the pulmonary artery to the aorta, allowing blood to bypass the lungs. In a duct-dependent lesion, the ductus arteriosus must remain patent after birth to maintain adequate systemic or pulmonary blood flow.

**Why the Correct Answer is Right**
In this scenario, the pediatrician suspects a duct-dependent lesion due to the child's failure to improve with supplemental oxygen. This suggests that the lesion is obstructing blood flow to the systemic or pulmonary circulation. The next step in management would be to ensure the ductus arteriosus remains patent to maintain adequate blood flow. This can be achieved by administering prostaglandin E1 (PGE1), a medication that keeps the ductus arteriosus open.

**Why Each Wrong Option is Incorrect**
**Option A:** Administering supplemental oxygen alone is insufficient, as the child's oxygen saturation is falling further despite this intervention.
**Option B:** The child's symptoms suggest a duct-dependent lesion, which requires intervention beyond mere observation.
**Option C:** Administering diuretics may not address the underlying issue of ductal dependency and may even exacerbate hypotension.

**Clinical Pearl / High-Yield Fact**
Remember that duct-dependent lesions are a medical emergency requiring prompt intervention to maintain ductal patency and prevent catastrophic consequences.

**Correct Answer:** B. Administer Prostaglandin E1 (PGE1) to keep the ductus arteriosus patent.