The Monkey in Nope went crazy because it was unable to control its anger after being labeled as lazy, and because of its frustration with its environment, which it viewed as limiting and inhibiting its potential. It was also having difficulty adapting to its new home in the circus after being taken away from its natural habitat.
As a result of all of this emotional turmoil, the Monkey went into a state of extreme agitation and exhaustion which threw the primates into a sort of breakdown that only resolved itself when it disappeared from its home.