The other answers are good, but they don't really point out the main reason why Yin Kurama did not reincarnate.
The Reaper Death Seal, or Dead Demon Consuming Seal is a special kind of seal. It not only kills you, but your soul is sealed inside the Reapers Stomach. By doing so, you are cut off from the Pure land.
From the entry on Bijuu
Because the tailed beasts are pure chakra, they cannot actually be killed; if they or their jinchūriki die, their chakra will re-coalesce in time. In addition, if a large portion of a tailed beast's chakra is separated from it, that chakra becomes a separate, sentient copy of the tailed beast.
This is the 2 bits of most important information here. First, Kurama was split in half, and the Yin half was sealed in Minato. This half was then taken into the Reapers Stomach, where it was sealed.
Now, as noted, they can not die. So why didn't the Yin half revive? Simple, Because they don't actually revive. As noted in the quote, their Chakra once dispersed due to death of some kind, will coalesce, giving them form again. However, the half sealed in Minato's soul was taken into the Reapers Stomach, and there it was sealed. There is no way for it to escape, and so it cant merge back with Yang Kurama, nor can it coalesce into its own half. Bijuu can not easily escape from their Jinchuriki, and the Reaper Death seal is like an incredibly powerful version of that.
so Tl;DR, Bijuu don't die, ever. They just disperse and coalesce. However, Yin Kurama was sealed into the Reapers Stomach, and not only could not escape, but didn't even disperse in the first place.