How do dolphins sleep without drowning? [video]
smithsonianmag.com
smithsonianmag.com
Not all of them will always sleep with one eye open, but at least a few in a group will in order to keep watch from coyotes, birds of prey and stray cats when they're not in the water.
Here's a direct link to bypass the advertisement: http://www.smithsonianmag.com/videos/category/ask-smithsonia...
Any animal without big selection pressures to develop and maintain this ability seems to lose it rapidly, as other adaptations of the brain for other purposes seem to preclude USWS. Only animals which really need it seem to have it.
What happened in at least one of these cases was dreaming with eyes open. From what I hear that might not be to uncommon but here I'm back to old wives tales.
You feel like time is missing because you have no recollection of that time - but that does not have to equate to you not being awake, or able to respond.