This reminds me of the story idea I'd love to see done for Keine x Mokou, where after the former dies, the latter waits for her reincarnation and so they cycle through again and again. After all, Mokou literally has all the time in the world, and having that to look forward to would keep her sane in the between times.
As to this story, I guess Reimu worked out a deal with the Yama and Yuyuko to allow their annual returns in a Dragonball Z kinda way.
That's been done, look up One Way Love Letter on this site.