Why did the Church of Jerusalem prosper while Paul's churches were so short-lived?
The Jerusalem church prospered because the Eleven, later the Twelve, stayed there year after year, continuing the ministry Christ began among Jews in Israel. Paul's churches were short-lived because Paul remained only a week or two in most places, though he stayed a year and a half at Antioch, then moved on.
Les explains that the Jerusalem church could prosper to a certain degree because the Eleven, and later the Twelve, came back and continued the ministry Christ began, staying year in and year out and working among the Jews in Israel. By contrast, Paul was not in any one place very long. Every place Paul established a church it was only for a week or two; Antioch was a year and a half, and Thessalonica perhaps only a couple of weeks, and then he moved on. Les emphasizes that apart from the miraculous working power of God, Christianity would never have gotten off the ground, because the people were steeped in idolatry except the Jewish element, who were steeped in Judaism. New believers fresh out of paganism made it only by that miraculous power, and Christianity began permeating the whole Roman Empire.