We know that through the entire year Hermione is using the time turner to attend multiple classes at the same time.
Do we have a definitive moment when we can see the effects of this impacting her negatively?
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The start of the second term seems to be when the increased workload (and lack of sleep) begins to take its toll.
Even so, he wasn’t showing the strain nearly as much as Hermione, whose immense workload finally seemed to be getting to her. Every night, without fail, Hermione was to be seen in a corner of the common room, several tables spread with books, Arithmancy charts, Rune dictionaries, diagrams of Muggles lifting heavy objects, and file upon file of extensive notes; she barely spoke to anybody, and snapped when she was interrupted.
HP: PoA (CHAPTER TWELVE – The Patronus)
"Negative effects" is somewhat relative. One could argue that having to ignore your friends because you are not allowed to tell them the truth is a slightly negative thing, so the first instance would be
“Well, I’m taking more new subjects than you, aren’t I,” said Hermione. “Those are my books for Arithmancy, Care of Magical Creatures, Divination, the Study of Ancient Runes, Muggle Studies —”
“What are you doing Muggle Studies for?” said Ron, rolling his eyes at Harry. “You’re Muggle-born! Your mum and dad are Muggles! You already know all about Muggles!”
“But it’ll be fascinating to study them from the wizarding point of view,” said Hermione earnestly.
“Are you planning to eat or sleep at all this year, Hermione?” asked Harry, while Ron sniggered. Hermione ignored them.
— Harry Potter and the Prisoner of Azkaban, Chapter four (The Leaky Cauldron)