This is the proper behavior of this type of skybox. You need to provide your map with a proper fog color, that will blend with the top of your skybox. That's because any other geometry will be hidden by this fog and skyboxes will always be visible. If you don't have a proper fog color it will look as if skybox hides your geometry instead of blending with it. In other words: it's not a good idea to keep your background color (which is the same as fog color) black unless you have a skybox or your skybox is black at the top and bottom. There is no real fix for that. Even a cubemap skybox will have such a behavior.
As for resolution - there is no real limit other than RAM you am at. Although I'd keep it at something like 256 by 512 or 256 by 1024.