BRUSSELS—A stalemate between the U.S. and other members of the World Trade Organization, including the European Union and China, stands to cripple the organization’s top court, threatening the global body’s survival.

On Wednesday the court, called the Appellate Body, will no longer have enough judges to rule on big trade disputes between countries.

At stake are international rules negotiated over five decades by the U.S. and Europe to boost global trade. The WTO, established in 1995, is the most significant outcome of that effort, helping to head off damaging cycles of tariffs and retaliation between countries. Now it’s stuck.

Efforts to modernize WTO rules for challenges such as China’s market-distorting state capitalism have repeatedly failed. Talks among its 164 members to regulate e-commerce and other new arenas have stalled for years. And a trans-Atlantic dispute over operations of its top court has sparked the split now threatening the organization’s core.

“The WTO is in crisis,” said Cecilia Malmstrom, who last month ended her term as EU trade commissioner. “If nothing happens, it will become irrelevant.”