Repeated P2004 DTC trouble code with no apparent symptoms

I'm having a weird issue with my 2004 Mustang 3.9L V6. I keep getting a P2004 trouble code and check engine light upon starting the engine. It won't come back on if I clear it while the car is running, but upon turning the car off and starting it again the code and check engine light will return. There are no apparent symptoms beside MAYBE using more fuel. Idle is normal at a stable 900 RPM. There's no apparent power loss. No loss in low-end torque that I can discern. No surging or rough idle. No hesitation with acceleration. None of the symptoms that are supposed to accompany this trouble code are present besides possible lower than normal fuel economy.

Any ideas?

I'm not even sure I have increased fuel consumption. I'm testing it now. I put 4 gallons in yesterday and I know what my usual MPG is. I set my trip odometer at 0 and I'm going to see how many miles it takes to get back to the same point on my fuel gauge.