After Ichika accidentally discovers Charlotte's true gender, she tells him she'll probably have to go home now that her cover's been blown, and probably be thrown in jail at best. So Ichika utilizes the IS handbook and reads the rule stating that any student attending the academy belongs to no nation at the time while enrolled, and tells her to stay there for now, so she can plan something within the three years she's there. Charlotte decides to keep attending, but this time as her true gender, although that draws the attention of Rin and Laura.
Laura right after Ichika saves her from her near meltdown mode. Chifuyu also tells Laura to seek her own path rather than try to follow in hers, and jokingly adds that she'd never be as good as her anyway (considering she blocked one of Laura's attacks with a BFS while not in an IS in an earlier episode). Laura becomes a Defrosting Ice Queen afterwards.
Rin breaking Houki from her Heroic BSOD after Ichika took the bullet and made her seriously question her desire to be a fighter after he called her otu on her refusal to help civilians (criminals, yeah, but still civilians).
Ichika giving a new ribbon to Houki and saying "Happy birthday." Her elation is pure awww.
In the second season's second episode, after a punishingly tough training session with Tatenashi, Ichika is so exhausted he can barely stay awake as he has lunch with the girls and they are all vying for his attention to go spend time with them. In the middle of their argument, he falls asleep. Cue all five girls giving us one of the most adorable moments in the series when they stop fighting and smile at his Sleep Cute status.
Tatenashi and Kanzashi at the end of episode 9 of season 2. The latter grew to despise the former, her sister, because she seemed to be The Ace at everything, and felt like she would never be as good. However, Tatenashi truly cares for her sister, and wanted to help her grow, and despite being beaten badly by an unmanned IS suit earlier, still manages to protect her sister from an attack, giving her enough time to get some Heroic Resolve.
In one of the few times Ichika gets to go an actual date with one of the girls, specifically Houki, he ends on a beautiful note. He says that though he started out being too caught up in everything and just going along, he says he was glad that he went to the IS academy, especially since he got to see Houki again. Of course he screws it up when he doesn't hear her love confession, but at least he lets her lean on him.
Chances of Chifuyu with her guard down are very few and far between but they are noteworthy. As much as she comes down hard on Ichika, it's easy to see that she's doing the best she can to protect him. There's also the fact that she skipped out on the championship bout of the 2nd Mondo Grosso in order to find him after he was kidnapped, while still wearing her IS.
It's a short-lived moment but after Ichika wakes up from his fight with Rin against the first Golem, Chifuyu is there, waiting for him to wake up. We then learn that she considers him her only family and that she'll find it hard to continue living if he were gone. This comes after her being so worried for him that she inadvertently puts salt in her coffee instead of sugar when the labels were clearly marked as such.
It's original material but in S2, the little slideshow of photos of Chifuyu and Ichika together when they were younger shows a side of their relationship that we don't usually get to see.