At the end, Shizuka did regain his memories after Yukihiko gave him the ring and put it on him. The reason they had a fight in the first place was because Yukihiko was feeling guilty of taking Shizuka away from having a normal heterosexual life. He could have a family, a wife and kids, but if Shizuka was with him, he couldn't. Yukihiko ultimately shunned Shizauka out without telling him and Shizuka thought he was cheating on him in the beginning, so the misunderstanding lead to Shizuka losing his memories and that's how we get this story.
Thanks! :3
You're welcome! :)
did the reason behind their argument explained? and did Shizuka remember his memories? .-.