The "eye" icon means that you should "look" through the forums for all the posts that already discuss this topic.
Unless Smart Stay is keeping your screen on when it shouldn't (which is unlikely, since it barely seems to have any success keeping the screen ON when it should), it's probably not responsible for any sudden decrease in battery life.
There are a ton of posts (hint, hint) about what is good/bad battery life, and how to track what might be causing battery issues, and what information to provide if you'd like help with a strange battery drain.
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