I don't think Shizune could have reasonably "figured out" that Misha slept with Hisao. I mean, it's possible, I suppose: she could have noticed Misha was missing on that night, asked around about her whereabouts, found someone who saw her going into the male dorms, and connected all the dots. But that's a whole lot to assume when there's absolutely no evidence for it in the game. I think you have to conclude that Shizune never finds about Hisao's infidelity, and decides to break up with him for other reasons.
So why did Shizune break up with Hisao? Well, I believe that even though Shizune never explicitly finds out about the encounter between Misha and Hisao, it still has a big enough effect on their own behaviors that it indirectly influences her in the end. The guilt of that single incident alters their group dynamic to the point where none of their relationships are reconcilable, and they all drift apart.
How and why does this happen? The story starts to diverge between the good and bad endings in Look Aside (bad route) and Look Ahead (good route), which both cover the morning and afternoon after Misha and Hisao's night together. First, some context: at this point in the story, Shizune, Hisao, and Misha have just had a vacation at Shizune's house, during which Shizune had sex with Hisao for the first time, but otherwise mostly ignored him to spend time with Misha. Then, they came back to school, and since then, things have been pretty awkward between all three of them. There was a fight between Shizune and Misha (not explicitly featured in the game, but talked and speculated about extensively by the characters) about their expectations of graduation, and they have a little less than friendly as a result. Simultaneously, Shizune has been reserved in dealing with Hisao, presumably because she thinks being openly romantic with him will be painful for Misha. Even more importantly, Hisao starts to act very weird on the morning of Look Aside/Look Ahead; he actually skips class to go hang out in the library, and Shizune finds him there. Hisao tries to excuse himself by saying he is sick, but I think Shizune sees right through that. Hisao refuses to tell her what's really wrong, and this lack of openness is very concerning to Shizune.
Now, to the part where the text starts to diverge. Misha confesses her feelings for Shizune to Hisao on the roof, and also expresses suicidal thoughts. If you're in Look Ahead (good ending), Hisao gives Misha a reasonably inspiring speech about the value of life, whereas in Look Aside, his response is not nearly as long nor as reassuring, because he is overwhelmed by the guilt of his recent actions. In fact, there is even a self-reflective comment by Hisao noting that he thinks his response is more for his own benefit than for Misha's, and I think the fact that this is pointed out in the text has to imply that Misha gets the same impression. So by the time Shizune interrupts their conversation on the roof, Misha is in a significantly different frame of mind depending on whether you're in Look Aside or Look Ahead.
Then comes the single most important decision made by Hisao in the entire route - yes, more important than his decision whether or not to sleep with Misha (although it is, of course, directly influenced by that earlier decision) - he either leaves the rooftop with Misha and Shizune for a nice afternoon together (in Look Ahead), or he uses a pathetic excuse about still not feeling well to leave them alone together and go back to the dorms (in Look Aside). The subtle long-term effects of skipping out on that afternoon cannot be overstated! Refusing to spend the evening with Shizune, and twice lying to her about his reasons for doing so, has a profound effect on Shizune's views on her relationship with Hisao. Based on that, she starts to think that Hisao is intentionally avoiding her and is unwilling to take their relationship seriously. At the same time, refusing to spend the evening with Misha has a profound effect on her, because it indicates that what happened between her and Hisao is too much of an issue for them to spend time together normally anymore.
Then, as Act 4 starts, the two paths of the story reconverge, as you attempt to deal with the issue of Misha growing distant from Shizune. Basically all the text in these scenes is the same regardless of what ending you're approaching, but the subtextual context of the situation is different, because Misha's frame of mind is different, and so is Shizune's. For example, in Grand Strategy, Shizune recounts to Hisao how, sometime after finding him and Misha conversing on the roof, she and Misha had another fight. Specifically, Misha told her that she is too selfish, confusing, and that she tries to bring people around her and then push them away. Even though her report of this encounter is the same whether or not you went through Look Aside or Look Ahead, you can assume that the reality of the situation was different depending on the context. In the frame of mind effected by the events in Look Aside, Misha was probably a lot more depressed and emotional when accusing Shizune of her shortcomings; possibly even angry. On the other hand, in the frame of mind effected by the events of Look Ahead, her accusations were probably at least somewhat more reconciliatory and heartfelt. In addition, Shizune's internal reaction to these accusations would be different depending on context! If Hisao abandoned her in Look Aside, then she would be much more worried about her relationship with Hisao during the rest of the day, and so when Misha starts accusing her of being selfish, and bringing people around her just to push them away, she would be inclined to apply those accusations to her treatment of Hisao as well, even if Misha didn't intend it that way. You can even see her repeat those same accusations as her reasoning for breaking up with Hisao in Terminal.
Now, during the subplot concerning Misha's distant behavior (i.e., the scenes from Grand Strategy to Parfait), Shizune has something to focus on aside from her relationship with Hisao. I think this is the reason those few scenes are so similar between the good ending and the bad ending; regardless of Shizune's thoughts regarding Hisao, and her worries about their relationship, she has a more pressing issue to deal with in the meantime. Unfortunately, if you took the bad route, Misha ends up being inconsolable, despite Hisao's best efforts in Parfait. Furthermore, as Present Tense (the first scene of the bad ending) begins, Shizune is avoiding class, Misha is still looking sullen, and Hisao is avoiding Misha. Shizune skipping class is actually a very important difference that demarcates the re-divergence between the good and bad endings. It occurs the day after the events of Parfait, which is actually a surprisingly fast response time. Based on how quickly after Parfait this difference occurs, I would actually speculate that if you're on the good path, and Hisao's attempts to comfort Misha are successful, she goes and finds Shizune to apologize for her recent behavior later that evening, whereas if you're on the bad path, she doesn't. Regardless, you can safely assume than by the time Present Tense begins, Shizune has decided that she has exhausted all options for solving her problem with Misha, and has concluded that the situation is hopeless. Shizune's absence from class indicates her depression at her failure to salvage her friendship with Misha, and is really the beginning of the end for her relationship with Hisao. Having to give up on Misha not only hurts her very deeply and causes her to reconsider her outlook on life, it also frees her focus to her worries about Hisao, which she had been repressing in order to deal with Misha.
Ultimately, failure at reconciliation with Misha, combined with Hisao's recent evasiveness and lack of openness, combined with Misha's own criticisms of her after the events of Look Aside, cause Shizune to conclude that her relationship with Hisao is similarly destructive and will end similarly poorly, so she resolves to break up with him. Both Misha's responses to the attempts to cheer her up and Hisao's distant behavior are influenced by their frames of mind that were fundamentally caused by their decision to have sex earlier in the story, and even if Shizune only felt the indirect effects of that decision, those indirect effects were enough to significantly change her own thoughts and actions.