The only real question here is whether South Korean politics is at a point where they'll choose to engage in this pointless kabuki theatre. Actually, South Korea is at this point better off if they continue to force the North to engage in pointless propaganda nuclear tests that use up some of the North's production than if they give the North a chance to build up their stockpile while engaging in meaningless talks that will last without result until the North feels the need to test again.
So you want them to keep testing? What happens then?
Kim's a megalomaniac, but he's not an idiot. He knows if he actually used a nuke, he's toast. At this point, there's no added danger from continued North Korean tests. Sometimes the best thing to do is nothing. This is one of them.