The song really ties together the “don’t give up” theme of the album. It gains a lot more meaning if the couple from this song is the couple who lost a child in Yuki no Furanai Hoshi.
For the life of me I couldn’t think of a reason why this is the last song in the album over Hero no Jouken. In terms of the story, Hero no Jouken provides closure on most of the songs. Thematically, it’s less clear that it’s about a cycle of heroes. Kono Hoshi no Birthday Song, however, very clearly represents the cycle of life (because childbirth). It brings the album full circle by reminiscing about when the world wasn’t ruined, while hoping the future will be different. Because of that uncertainty planted in the child, we know that something will happen to them, we just don’t know what (it’d be cool if the child became the boy from Hero no Jouken).
See Hero no Jouken would’ve been better as a last song