BEIJING—Vice President Xi Jinping's continuing absence from public life is throwing another wrench into preparations for China's leadership change this fall when Mr. Xi is due to take over the nation's top job, according to party insiders, analysts and diplomats.

The announcement of when the meeting to start the transition will take place is already considered late, after a highly unusual year in Chinese politics, and Mr. Xi's disappearance, apparently because of a health problem, has created another complication that could...