Bottom eyelids disappear in object mode

I was unhappy with the eyelids I made following a tutorial here: https://www.youtube.com/watch?v=c1UrNFJS2ns I finished the tutorial series, but I wanted to go back and replace the eyelids and make them rotate using bones centered in the eyeball (instead of shape keys with driver bones). But since I distorted the eyelids to make them fit over the eyeball (when using the shape key method), I deleted them and started to make new ones. I turned off all the modifiers, and I disabled the Basis shape key (eye icon). Following the tutorial, I added a mirror modifier, I then added a sphere to the center of the eye in object mode scaled it to fit a little over the eyeball. I then joined (ctr J) it with the body mesh. In edit mode, I deleted half of the sphere, extruded the edge of the top lid to simulate thickness. I then duplicated the top lid and rotated it around the center of the eyeball 180 degrees to make the bottom lid. And it looks okay in edit mode. But when I go to object mode the bottom lids disappear. Can someone tell me what I am doing wrong?

In Edit Mode

http://i846.photobucket.com/albums/ab27/blanco1111/help27_zpsb23e5be3.jpg

In Object Mode

http://i846.photobucket.com/albums/ab27/blanco1111/help28_zps6eb4b248.jpg

Blender File: http://www.pasteall.org/blend/28091

The lower eyelids only appear in the smile.L Shape Key, I think for all the other shape keys it goes back up to the same position as the top eyelid.

To get it to appear again: I tabbed into edit mode, the lower eyelids were already selected. Pressed P to separate the lower eyelids to a new object (Tim_mesh.001), Then for that new lower eyelids object delete every shape key that is not smile.L.

With smile.L as the last shape key, go ahead and delete smile.L, you should have no shapekeys on that object, and the eyelid should be in the same place as it was for smile.L (aka, where it should be).

Now select the lower eyelid object, and then the Tim_mesh, and press Ctrl J to join the two objects. Now the lower eyelid should appear the same across all the shape keys. You may need to re-fix it per shape key to match your desired expressions, but at least it’s visible now.

Thanks for responding. The good news: I was able to follow your instructions. The bad news: The eyelids are still an issue. I can’t get the bottom lids to roll up on the eyeball without going through the eyeball itself. I thought by using a bone directly instead of shape keys with bones as drivers, I might get better results. I don’t understand why the bottom lids do that, but so be it.

http://i846.photobucket.com/albums/ab27/blanco1111/help29_zps52e52d95.jpg