One possible reason could be that Naruto realizes Sasuke is too far gone in his quest for revenge. Naruto might see that no matter how much he tries, Sasuke won't change his ways, so he gives up. For example, if Sasuke keeps attacking innocent people in his pursuit of power to defeat Itachi's enemies, Naruto might finally lose hope.
Sakura could also be more composed in her reaction. Given her growth as a character, she might try to reason with Sasuke first. She could say things like 'Sasuke, I know you must have a reason for this. Let's talk about it.' However, if Sasuke doesn't respond or seems hostile, she may start to feel betrayed. She might then use her medical ninjutsu knowledge to try to find a weakness in the snakes or in Sasuke's technique that is keeping her tied up. She could also start thinking about how she can turn the situation around and make Sasuke see reason.
One possible reason could be Sasuke's continued obsession with revenge. His single - minded pursuit of power and vengeance might make Sakura feel neglected and unloved in the relationship. For example, he often goes off on long and dangerous missions alone, leaving Sakura behind worried sick. Another reason could be a fundamental difference in their values. Sakura values life and healing, while Sasuke has been more focused on destruction in his quest for revenge.
Sakura might grow tired of Sasuke's cold and distant behavior. In fanfiction, she could realize that she's been trying too hard to hold on to a relationship where she's not getting the love and attention she deserves. Maybe she meets someone else who shows her more care and respect, which makes her consider breaking up with Sasuke.
In fanfiction, Sasuke could start by giving Sakura a sincere apology. He might bring her rare flowers from his travels, as Sakura loves nature. Maybe he could also take her on a special mission where they can work together closely and he can show his trust in her abilities.
Well, it could be that Sakura finally decides she's had enough of Sasuke's brooding and cold behavior. Maybe she stands up to him about his disregard for the village or his lack of communication with her. She might tell him that she's her own person and won't tolerate his dismissive attitude anymore.
Sakura would likely become more confident. Standing up to Sasuke means she's no longer the meek girl who just follows him around. She'll start to trust her own judgment more.
In some fanfiction, Naruto could give up on Sasuke if he falls in love and his new relationship makes him see things differently. His new partner might convince him that Sasuke is a lost cause or that he should focus on their own future instead. Also, if Naruto suffers a major setback in his own life, like losing a dear friend in a fight related to Sasuke, he could lose the will to keep chasing Sasuke. This would be a very emotional and complex turn of events in the fanfiction world.
One possible storyline could be that Sakura realizes Sasuke is too consumed by his revenge and she decides to focus on herself. She might start training harder to become a better ninja in her own right, perhaps specializing in medical ninjutsu even more. This could lead to her making new friends and allies within the village, and she could end up being a key figure in Konoha's development, without Sasuke in the picture.