Now that is just sexy. I've heard that smarter people are easier to hypnotize. So I guess Kagami is especially susceptible to hypnosis. I also think it's sexy how she tries to fight the urge to be hypnotized. But as her eyes keep following the coin, she starts to become drowsy, her eyelids get heavier and heavier, and she can no longer think of anything else. So she keeps following the coin with her eyes, which are by then nearly impossible to keep open, becoming sleepier and sleepier until finally, she just gives in to the drowsy feeling and closes her eyes.
I have a theory, that the hypnosis didn't work and that Kagami confessed her love for Konata out of her own free will and used the hypnosis as a sort of benevolent self-deception on herself to summon the strength of will, since even if the hypnosis would have taken hold of Kagami, if her feelings were that of non-romantic friendship than of romantic love, she would express them differently.