I keep searching for a story I found online, but I can't find it. It was a free published story (episodic) about man trapped in a time loop, with loop starting with his sister doing some mischief to him and then him leaving for some kind of university. He then joined forces with arachnid-like creatures under the university and helped then retain their memories after each loop. There were also some other time traveling man, which was trying to succeed in escaping or something. The protagonist keep concealing that he too is traveling, but in the end they joined forces and found out that they are in some kind of simulated loop, separated from the real one and that they must escape or they will be destroyed with it.
Oh, I finally found it, it was Mother of Learning https://www.fictionpress.com/s/2961893/1/Mother-of-Learning
It starts with protagonist (Zorian) at his home being waked up ("Morning, morning, MORNING!") by his sister, who then starts being even more annoying. He then travels to The Academy to resume his studies. The story then continues for maybe two months but then suddenly an invasion in which one attacking lich that Zorian encounters tries to destroy the soul of the "original time looper" (one of protagonist's classmates that was below average the previous school year, but is suddenly excellent in everything), but accidentally binds it with Zorian's. Then both of them die and Zorian wakes up again to "Morning, morning, MORNING!". In some loop later when on dungeon exploring he encounters psychic arachea that begins his training in mind magic and asks him to store some memories for them so they can be aware of passing loops.