SAN FRANCISCO—A $100 million fix to stop a San Francisco luxury high-rise from sinking and tilting even more is on hold while engineers try to learn why the building has sunk another inch (2.5 centimeters) during the repair. Doug Elmets, spokesman for the Millennium Tower, said in a statement that pile installation to beef up the building’s foundation is on hold for two to four weeks as they try to understand why the “increased settlement rate and available means of mitigating this.” Elmets said the building is safe, the San Francisco Chronicle reported Thursday. The 58-story tower opened to fanfare in 2009 and all 419 apartments quickly sold out. High-profile residents have included former San Francisco 49er Joe Montana, late venture capitalist Tom Perkins and Giants outfielder Hunter Pence. But by 2016, the building had sunk 16 inches (40 centimeters) into the soft soil and landfill of San Francisco’s dense …