I think what might be happening here is that the sides of the box are very rectangular (rather than square).

If you draw a box that has square ends, then if you turn the box so the ellipse faces you directly, you'll be looking at a circle inside of a square. As you turn that plane in space, the circle will turn into an ellipse. The minor axis will cut it in half as you expect. (Like you see here: https://www.carbodydesign.com/tutorial/13560/drawing-car-wheels-in-perspective/ )

However, if you have a box with rectangular ends (like a cereal box or a book), you would have to draw an oval (not a circle) inside it to touch all the edges of the rectangle. As the plane of the box with an oval drawn on it turns in space, it doesn't obey the rules of a circle turning in space. There won't be a minor axis cutting it in half. I think that's what you have going on.

It's hard to draw a perfect square in perspective, but I think the goal is to get close-ish here. Close enough that the ellipse is somewhat convincing. Maybe it's easier to start with the ellipses for a few, and draw the boxes around them until you get a feel for it?