As Jeb Bush heads to Texas on Sunday to rally top fundraisers along with his father and brother, former presidents George H.W. Bush and George W. Bush, the family’s vaunted financial network is mostly disengaged and splintered—and his campaign stock is falling. The one-time front-runner for the Republican presidential nomination is roughly tied for third place among GOP contenders in campaign cash and has fallen to fourth or fifth place in national polls, including the latest Wall Street Journal/NBC News survey. His crowds are modest. He failed to dominate in either of the GOP debates, and million-dollar ad buys in...