According to the plot of the serie, Sai realized his role was not to achieve the Divine move (also called "hand of god") but that he was just there to transmit all his knowledge of the game to Hikaru. Having no more regrets, he can leave the world. So Madara Uchiha's answer is correct.
Also, in a public interview Yumi Hotta (scenarist of the "Hikaru No Go") gave during European Go Congress 2011 (in Bordeaux, France), someone asked her "Why did Sai disappear?". She answered that Sai had a role similar to a father to Hikaru, and that you cannot live your whole life with your parents following you. At some point, you have to grow up and become an adult. So, the fact that Sai disappeared is a symbolic way of saying that Hikaru is (on his way to) becoming an adult.
Hikaru "finds" Sai later when playing go. This has the same meaning as saying that even if you leave your parents, you will always have in you what they told you, what they taught you, and the values they transmitted to you.
And, in fact, by the end of the series Hikaru looks a lot more mature than when he was with Sai.
According to Yumi Hotta, "Sai had to disappear", otherwise he would be blocking Hikaru from becoming an adult, in the same way a mother or a father would if he or she was always protective about his/her child.