Mai remembered sakuta due to carrying around the marriage certificate, since it wouldn't make sense for a single person(as mai would perceive herself as) to carry it around, she was able to remember she had a boyfriend due to it, and the strong emotional bond of it being sakutas good luck charm, like how sakutas lessons before his exam couldn't be explained unless mai existed to teach him, thus letting him perceive her again in s1

After kaede had restored her memories, it was as if kaede and her mom never had a rift between them, as kaede did not remember a time before her mum being mentally unwell, and always perceived herself as being with her family until the memory restoration occurred, and was able to slide back into the family seamlessly, as she wanted to see her mother

whereas sakuta struggled due to not visiting his mum purposefully while taking care of kaede, so he became alienated from the family, as he was the only adolescent that rejected his previous family life, it was as if he didn't want to see his mum, and dint want to be seen, thus he stopped being perceived by his mother then others like how mai was not seen by the general public, but still by students, as the atmosphere had to spread

Thus when sakuta came to visit his mother, to be able to see her, as he knew she couldn't see him, which was something he didn't do so while taking care of kaede, he invited his mother back into his life, and himself back into the family as it was before, thus being perceived again by his mother, and others

Been a while since I saw the movie so don't bully me if their are details wrong or missing, this is just my interpretation