How many miles will pass before check engine light recycles and goes off due to the fuel cap not being on properly a 2004 mercury mountaineer?

There's no set mileage for a check engine light to go off after a loose or missing gas cap on a 2004 Mercury Mountaineer (or any other car). The light will typically stay on until the problem is fixed (the gas cap is tightened) and the car's onboard diagnostic system (OBD-II) detects that the problem no longer exists.

The system usually needs a few driving cycles (meaning starting the car, driving for a while, and turning it off) to confirm the problem is solved before it turns off the check engine light. This could be as little as one driving cycle or a couple of days of driving. Mileage driven is irrelevant; it's about driving cycles and the system detecting that the fault has cleared.