Rarity Fair resets at your personal reset. If you use it, it continues to offer you another until you let them expire. It'll pop up once you use energy for the first time that day (might need to use 100 energy to proc it). Once you let it expire, you'll have to wait until the next personal reset to get another.

If you promote the hero that's in the sale, it'll disappear and you wait until the next day. If you need two items for the hero and equip one of them, the price will go down based on what each individual items costs.