New cotton has a little finish left from weaving. One cold wash before you sleep on it softens the fibres and settles the colour.
Skip the fabric softener. It coats cotton and makes it less breathable over time. A half cup of white vinegar in the rinse does the same job without the film.
Dry in the shade or tumble low. Strong midday sun fades colour faster, especially deep shades like Kaapi and Anar.