As others have Said, leaving on for over a week makes the polish more difficult to remove, hence the pigments that are released during removal get rubbed into the nail plate. This is when staining occurs, especially on dry or damaged nails.
Cuticle Away is very good at lifting staining, have you tried that?
In future, I would remove no later than 7 days after application. Some find that putting a very sheer colour down first helps stop staining, eg Lavishly Loved.