I think both the MC Satoshi and Rin actually travel back to the past together which is why Rin started acting differently from before in the second take. There were quite some parts in the manga that hinted on this.
Both Satoshi and Rin didn't realized that each other have past memories, so they both missed out on the opportunity to confirm their feelings with each other and start dating. A bit sad that MC couldn't confess his feelings to Rin in the end of the second take, but I can understand why he didn't do it. I felt that by not confessing, it makes the story richer and the plot feels more whole and complete.