Wiktionary
lose their head
vb. (alternative form of lose one's head English)
Usage examples of "lose their head".
It is said of the French that they don't usually lose their head, but when they lose it they lose it well.
He was dead wrong, but you know anybody's liable to lose their head if you ride them thataway.
He just hoped that when the showdown came at Andrews, nobody would lose their head or start overreacting in the ways that get people killed.