I think because Min-Soo really loyal to Yona. He even help her escaped when Soo-Won tried to kill her. Min-Soo may act in his own to help Yona ascend the throne..
thought the same thing. i immediately thought min-soo was giving him poison little my little in his own way to get revenge and help yona? but I bet he got a limited lifespan because of some illness or something
Either Min-Soo drugged him, or Soo-Won really don't have much time left