Interesting question... I think, it's a combination of several problems leading to "dead eyes". Small pupils and lot's of visible white do make eyes look glaring, cold and unemotional, like in the Lili example above. Did you know, that in pictures models' pupils are often photoshopped larger, so they look more attractive and approachable to the viewer?
Another very important thing is blinking. A fair amount of blinking appears to be human, it's also something that we perceive as attractive. In the scene of the Until Dawn video, that I was referring to, the character hardly ever blinks. He's just creepily staring at us. Only dead things don't blink!
Then there's also lots of muscle movement and twitching going on around our eyes and in our eyes. Did you notice, that eyes/irises never really stand perfectly still? Dead or Alive 5 does this very well. Go zoom in on a character during a victory pose and watch how vivid the eyes actually are. It's also something, that we see a lot in anime. The flickering lights in the eyes, especially if a character gets emotional, are supposed to bring movement into the eye.
Speaking of flickering lights: Reflective lights also bring a lot of life to eyes. They add a focal point and bring movement as well as the simulation of wetness from tears to the eyes. Which, again, we perceive as natural and human. When I do character illustrations, placing highlights/shine in the eyes is always an important, if not the most important, step in the entire face. Here's a recent illustration of mine with and without the highlights:
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It's such a small thing, but the difference is huge!