If you switch over to the screen with speed, distance remaining, and instant fuel economy (one screen up from the one displayed on your DIC in the picture), does it go up when you fill the tank, even though the needle stays stuck?
If the DIC distance remaining is accurate, but the needle is wrong, you most likely have a problem with the stepper motor in your instrument cluster.
If the DIC distance remaining is inaccurate in a way that corresponds to the stuck needle, you most likely have a problem with the level sensor in the tank.
If neither of those is the source of the problem, then there's probably an intermittent wiring fault between the level sensor and the ECM.
Since it always sticks at the same spot, I'm heavily inclined to think it's the stepper motor behind that fuel gauge on the instrument cluster. There's probably a dead spot in that stepper motor, and a jolt from a bump or a surge of power jars it loose until you get back to that spot and it sticks itself again.