"Endless Eight" is a short story from the light novel The Rashness of Haruhi Suzumiya, written by Nagaru Tanigawa and illustrated by Noizi Ito. This story takes place in the August of Kyon and Haruhi's first year of high school, after "Remote Island Syndrome". The "Eight" in the title refers to August being the eighth month.
Haruhi wishes to pack the last weeks of summer with typical summer activities such as attending an Obon festival, lighting fireworks, going to a swimming pool, getting summer jobs, and bug hunting. One night, Kyon receives a phone call from Mikuru and Itsuki telling him to meet them. There they, along with Yuki, inform him that time is looping over the same two week period again and again. Kyon and the other SOS Brigade members simply experience déjà vu because of this, except for Yuki, who has complete memories of every iteration of this loop. They suspect that Haruhi has no conscious knowledge of any of this. To make matters worse, according to Yuki these two weeks have already looped more than 15,000 times, coming out to nearly 600 years of summer. They theorize that Haruhi must be unconsciously looping time because she doesn't want the summer to end, she doesn't feel like they've finished all of their summer activities. Eventually, a desperate Kyon suggests they finish their summer homework together. The SOS Brigade has a homework party, and time returns to normal.
The anime adaptation of this story is notorious among anime fans for being so very very very long-winded. In what could have taken two or three episodes, the animators decided to use eight episodes to tell the story, using the same dialogue and situations but reanimating them every time with subtle differences. This was meant to instill in viewers the same feelings Yuki must have had, reliving the same thing week after week after week. Naturally, most people were tired of this by at least the third or fourth repetition.