BEIJING—The volley-for-volley trade war between China and the U.S. is accelerating at a time when Chinese President Xi Jinping can ill afford to make concessions, raising the likelihood of a protracted struggle between the world’s two biggest economies.

Mr. Xi is ordering a celebratory run-up to the 70th anniversary of the People’s Republic in October, an event that Communist Party watchers and media say will showcase him as a strong leader of a powerful nation. With his government struggling to rejuvenate a sluggish economy...