Sometime, newborn kittens' eyes will remain closed, or partially closed, for several weeks. However, to play it safe, it is best to take your kitten to a vet, just to make sure that s/he doesn't have an eye infection.
I have a Purebred Himilayan cat and this happens all the time. Use cotton balls available at any drug store. wet them with lukewarm water and wipe their eyes daily.