TOKYO (AP) — North Korea's collapse has been predicted — wrongly— for decades.

Some said it would happen after fighting ended in the Korean War in 1953. Others thought it would be during a 1990s famine or when national founder Kim Il Sung died in 1994. And when the death of his son, Kim Jong Il, thrust a little-known 20-something into power in 2011 some felt the end was near.

It's no surprise then that recent rumors that leader Kim Jong Un is seriously ill have led to similar hand-wringing.

South Korea believes that Kim is alive and in control, and most analysts agree that even if he weren't,...