Carthage's 2nd Punic War went to hell when Hasdrubal's reinforcement army was defeated in Spain.
As others have mentioned, the Gallic kingdoms were pretty much screwed by the time Rome came around since they had weakened themselves through centuries of civil war. Same for the Successor states.
Napoleon's empire went to hell when he decided to invade Russia. Germany's empire went to hell after they decided to invade Russia and declare war on the US.
Hideyoshi's invasion of the East Asian mainland was doomed before it even began because he was dumb enough to think he could conquer the Ming Empire.
Eastern Han Empire went to hell when the central authority gave too much power to military governors.
Roman Republic went to hell after the Sulla-Marian civil war, then Caesar-Pompey civil war, then Conspirator-Loyalist civil war, then Octavian-Anthony civil war.
Humiliating a Mongol ambassadors was medieval equivalent to telling the US military to "drop a nuke on me."
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