We examine how categorical economic policy uncertainty (EPU) is linked to extreme downside risk in U.S. energy futures markets across contract maturities. Using data from 1994 to 2024, we document maturity‐dependent spillovers between EPU indices and Value‐at‐Risk (VaR) for crude oil and natural gas. Crude oil VaR exhibits increasing connectedness with maturity, while natural gas shows a flatter pattern. The composition of policy‐driven spillovers also varies across maturities and time. Storage capacity constraints, which may hinder carry arbitrage, intensify spillovers to longer‐term contracts, especially in the oil market. This highlights the role of physical market friction in policy risk transmission.