Technically, the DPRK and South Korea have never stopped being at war. In fact, only North Korea even signed (along with the US and China) the armistice agreement in 1953 - the South Korean government of the time refused.
That being said, I'd say it's pretty unlikely there will be any organised attempt to restart the conflict, since absolutely no side stands to gain from it. Seoul will become a smoking crater, the North will eventually be overrun (and the South doesn't really want them, given the economic drag they'd put on the country, especially after the devastation of another conflict), China will lose its nominally friendly border, and the US does not have the money or manpower to get involved in another massive conflict. Kim Jong Il likes throwing out provocations and shifting stances, but both he and his father were pretty good at knowing when to push and when to (insincerely) back down.
That being said, I'd say it's pretty unlikely there will be any organised attempt to restart the conflict, since absolutely no side stands to gain from it. Seoul will become a smoking crater, the North will eventually be overrun (and the South doesn't really want them, given the economic drag they'd put on the country, especially after the devastation of another conflict), China will lose its nominally friendly border, and the US does not have the money or manpower to get involved in another massive conflict. Kim Jong Il likes throwing out provocations and shifting stances, but both he and his father were pretty good at knowing when to push and when to (insincerely) back down.