South Korea's population will be cut in half in less than 50 years and be right around the size of North Korea by that time, which will have a much larger army unless South Korea dramatically increases conscription.
Within 70 years, South Korea will cease to be a functioning society. Their options are to dramatically and abruptly increase immigration (overtaking their native population and thereby wreaking havoc on their culture), reunify with North Korea (whose population would overtake theirs), or just give up and accept fate.
Either way, they're going to be overrun or die out in the long run, and it'll only get harder for working age people. Not sure nuclear armament is the best strategy given the demographic realities...