SINGAPORE—Surging military spending across Asia has made it the world’s second-biggest region for such spending over the past decade, but U.S. companies, the biggest sellers of military equipment, are struggling to take full advantage of that growth, even as revenues back home stagnate. Demand in Asia for defense equipment—and calls for greater U.S. military involvement—have grown as China’s display of military might in the South China Sea intensifies regional tensions. Total global spending on defense in 2014 was $1.719 trillion, of which Asia and Oceania contributed $423 billion, or 25%, behind only North America’s $596 billion, according to the Stockholm...