Hi! I'm from the United States and have only heard that phrase used in reference to cars/automobiles. Where did you hear this phrase?

This expression means not all is running well. If a car slips out of gear, what would happen? The car will be chaotic, stall or break down.

Um carro que possui um motor padrão, no qual você precisa usar um "câmbio manual" para passar pelas diferentes marchas ao dirigir. Às vezes, as engrenagens do motor ficam velhas e gastas, e o processo de mudança entre as engrenagens e velocidades diferentes torna-se difícil ou não funcional.

To become out of control.

I don't think that phrase is used as an idiom because it isn't clear what the cause or effect of the slip is in a way that could be attached to a generic situation. If I interpret it to mean "sudden failure with a chance for recovery", and it refers to a person, then I would instead say they "dropped the ball". If it refers to a system, then I probably wouldn't use an idiom and instead talk about how it malfunctioned or had a glitch. Without context, it's hard to tell.