Higurashi no Naku Koro ni Kai, Suzumiya Haruhi no Yuuutsu (2009) Recommendations
Although Higurashi is less repetitive, both are second seasons with the idea of an 'eternal summer', only one person who remembers all of it, deja vu with the other characters, and a 'god' behind all of it.
The similarity shared with Endless Eight becomes apparent late at season 1 - with Rika being the keeper of time, and resets time in order to reach a happy ending, similar to the role for Yuki. Other characters eventually pass over memory between other loops and help to change fate. Even though being a Haruhi fan, I must say that Higurashi executes this much better in comparison.
Both series feature mysterious elements such as aliens and infinite time loops/infinite summer/Endless Eight.