For a remarkable assortment of Christian leaders, the answer has been "create a new church or organize major reforms of the old one." Even stranger to me, some of these reforms have focused on education. "There aren't actually going to be any future generations, but let's throw all our efforts into building schools for them anyway."
In the 20th century we have the example of the Jehovah's Witnesses, which sprang from the teachings and calculations of Charles Russell. Russell worked out that the "time of troubles" preceding the End began in 1914, a belief still widely held by Jehovah's Witnesses and many others; motivated at least partly by the impending end, the Witnesses have launched a very effective worldwide missionary effort. And of course there were Jesus' original Apostles, who believed the End would come within the time of their lives and created the Christian church.
Whatever it is, maybe the strange motivational effectiveness of these beliefs helps to explain their persistence despite thousands of years of false predictions.