2 things.
First: When AH first loads, go offline and bring up the clipboard. Click "Options" then "Graphic Details" and try unchecking "disable other plane skins".
Second: Go to the hangar and check the "download skins in the background" option.
Now choose the Plane you want. Look for a skin there. You have to scroll up and down to look for them all, hit the arrows, because the slider doesn't always reflect the current location of the skins pop-down window.
Make sure you scroll up and down to see all of the skins, and see if the skin you want isn't off the edge of the scroll box.
It might help if you took a screenshot and posted it here. Show us what your skins drop-box looks like in the hangar.