ERBIL, Iraq—The Kurdish capital is built on oil. From the high-rise apartment blocks that ring the broad outer boulevards, to the streetside jungle gyms and gleaming Dodge Chargers driven by local police, almost everything in Erbil is derived from the region's energy riches.

Until recently, this oil and gas bonanza seemed like the final piece in the Kurds' long-standing bid to carve out their own state in northern Iraq. While the rest of the country leaped from one outbreak of violence to another after the toppling of dictator Saddam Hussein in 2003, the three self-governing Kurdish provinces reeled in foreign firms to tap their natural resources and used the proceeds to build the infrastructure of a prospective nation.

The 40 percent drop