I'm asking about the Great War. The Russian army famously "voted for peace with its feet"; but before they did, they'd battered the Austrian army to the point where much of its front just gave way to the Brusilov offensive. The Italians essentially collapsed at Caporetto and never really recovered; it's just as well for them they were fighting the Austrians who were not in much better shape.
The French had their mutinies after the Nivelle offensive; and even the Germans finally surrendered in part because their army was refusing to hold the line any more, although some units fought stubbornly until the end. How did the British avoid this? They were in it from the start, and mass-mobilised from sometime in 1915; so it's not a question of having been a short time in the war, as with the American army.
Although I don't know much about the specifics of British morale, most armies had more or less similar morale issues overall (although I'll grant that they were strongest in the ethnically divided Austro-Hungarian Empire).
The Italians, for their part, were able to recover after Caporetto in part because the man in charge of the front, the legendarily incompetent Field Marshall Luigi Cadorna, was replaced by Lieutenant General Armando Diaz. The original plan had been to give Cadorna's job to the King's cousin Amadeo, the Duke of Aosta (who had distinguished himself as General of the Third Army). However, King Victor Emmanuel, jealous of his cousin, vetoed the decision. The compromise has surprising positive side: the Lieutenant General Diaz had been closer to the action, and implemented a number of morale-saving initiatives (in addition to having directly served under Aosta in the third army, who was the most competent Italian tactician by a longshot). I actually wrote about them about a year ago, you can read the answer here.