Is it possible to color match the paint color to the old one on the wall so well, that it will be unnoticeable?

When the wall is scratched, got dirty, or drywall repair has been done, a home owner is looking to touch up the area that stands out. Many home owners try to color match the paint so the touch up can be done in the middle of the wall, and there is no need to repaint the whole wall. In some cases it would be possible. One can cut out a small piece of drywall that has original paint on it, and take it to a paint store to get a color match. Most likely it would take multiples trips to the paint store, as first match (or even first few matches) will not blend in with the original color. It is possible to achieve a decent match but it would be very time consuming. Paint fades over time, the walls get dusty. New paint applied over drywall with old paint will be noticeable regardless of how well the color was matched.
Another reason it is so difficult to match the paint for a touch up in the middle of the wall is the difference in paint sheen. Even the paint from the same paint store will have different sheen, if a different product is used. For example Dunn Edwards' Versasatin (satin finish) paint has 12-17% sheen and Suprema low sheen (which is also satin finish) has 6-8% sheen. Usually that small of the percentage will not make any difference to a naked eye, if the whole room or even one wall is painted, but in case of a small touch up in the middle of the wall will show instantly.
The only good solution to a touch up problem would be to repaint the whole wall from one corner to another.