Currently Airing Anime

@smooth

 Spoiler

I agree that regret plays a pretty big role in her despair, but it's clear that she gave up on Kamijo and that Kamijo is probably the leading cause for her despair. Like I said, Hitomi presents her a choice and Sayaka definitely has the ability to choose to be with Kamijo. However, Sayaka has already thought out about what might happen if she were to be with Kamijo. What Sayaka believed would happen was how in a similar sense to how Kyouko's dad responded to Kyouko's secret, what Kamijo might feel that he wouldn't be able to love her and might see her as inhuman- ultimately leaving her alone and losing the thing that mattered to her the most. Sayaka feels like she's already in a losing situation, choose to be with Kamijo and what she fears may actually happen or choose not to be with him, and she will not be with him. But Sayaka didn't even try, she essentially let Hitomi confess. Who knows? There's always the possibility that she and Kamijo could have overcame her condition and he might have been to still love her. But to just not try at all, it means essentially gave up, but also, she gave up because she felt that rather than be hurt in the future or hurting Kamijo, she decided to abandon a possibly failed future of if they are to be together (interestingly, doing something that diverts from what Kyouko did. By cutting herself off, no one else had to be hurt, but the consequence is that she hurts herself in the process). She gave up on Kamijo because she felt it was impossible for her to be with him, and consequently, her giving up leads to her losing all motivation to survive- or despair; and continues self-destructive behavior until she eventually became a witch.

I don't think it was that she "gave up" but rather that she saw herself no longer suited to be with Kamijo. It didn't matter if Hitomi's offerred a chance for her to claim Kamijo or not because she did not have the humanity to do so. At which point, she felt no different than Frankenstein or the Hunchback of Notre Dame, a freak shunned by society as she had even said so herself when she called herself a 'zombie'.

As for the stalking scene, we already had a sense that she'd given up; but what brought her there is that subconsciously, she still holds on to some hope and expects Kamijo to be her knight in shining armor to save her from her spiral into depression and loneliness.

On the contrary, that scene was shown to convey that she had not given up. Because she felt she cannot be with Kamijo, she can only watch him from the shadow and regrets what her decision cost her what she could have had. While she was in her despair, she still continued to love him. If she had given up, she would not have stood up to those womanizers on the train. The fact that what they did to their girls agitated her because their actions would only bring the pain she feels to their girls and she made it clear that she would prevent that. So it's not that she gave up but more that she is at a total dead end.