China keeps North Korea alive because china sees North Korea as an indispensable tool in an unequal struggle with the US over influence in their own back yards.
Therefore they will hardly concede North Korea to us and thereby concede even more influence to us in their own backyard without extracting a commensurate price from the US. For them the commensurate price is America giving up positional or alliance advantages such that the relative balance of power between the US and china would become more equal even after china gives up North Korea, than before.
What is America willing to give up that is worth more to america's relative position compared to china, than North Korea is worth to China's relative position to America?
The answer is almost certainly nothing. So there is no diplomatic solution to this impass.
Therefore they will hardly concede North Korea to us and thereby concede even more influence to us in their own backyard without extracting a commensurate price from the US. For them the commensurate price is America giving up positional or alliance advantages such that the relative balance of power between the US and china would become more equal even after china gives up North Korea, than before.
What is America willing to give up that is worth more to america's relative position compared to china, than North Korea is worth to China's relative position to America?
The answer is almost certainly nothing. So there is no diplomatic solution to this impass.