Lets try this ONE more time.
When you save an image, all it saves is a flat image. If you made some stupid loving white layer to make the black seem to disappear, that gets flattened into it. AKA There's no longer an extra white bar, it's part of the background.
If you need more explanation, I'll loving kill you. I'm still having some stupid loving problem where it won't animate after I saved it.
Aha, but it seems that you do not know how .gif files work.
They animate by layering frame over frame. If you layer over a transparent layer, then the previous frame is unchanged, and in this case there is no white to overlay over the eyes in order to make them blink.
That's the problem you're having, and is why it won't animate.
Plus if you open up the .gif image in an editor such as GIMP, the layers are still there, and it's not flat.