The difference between Dame and Kanye is that Dame was in front of Jay-z. He ran things and Jay never liked that. Kanye (thus far) has been an obedient student and even so, Jay has reached iconic status where he can't be touched or brushed by any rapper alive. So to say that the falling out between Dame & Jay is something that could potentially happen to Kanye & Jay is stupid.
To answer the thread's question, they most likely never will. They have a symbiotic relationship, both of them benefit mutually from having each other around, and there's no clashing ego's to separate them apart. Either way, the only reason Jay snaked out all his former pals is cuz he was trying to get to the top, but it's obvious that Jay in 2013 doesn't care about that anymore. Matter of fact, Jay is willingly passing that torch to Kanye.
Let's not forget, the people that Jay have fallen out with were either people who fired at Jay in the first place due to envy, jealousy, whatever or people that conflicted with Jay's agenda and needed to be removed. This is why Jay-Z is the President of hip-hop, he can play the game. Kanye seeks no such goals and is intent on making good music and good music period. Jay is in his 40's, you think he still has that same mindframe?