The usual expression is 'out for the count'. It's a term that comes from the sport of boxing. If a competitor is knocked to the ground, the referee starts counting. If he is still on the ground by the time the referee stops counting, he is disqualified. We usually use this to mean that a person is very soundly asleep, or perhaps too drunk to stand up. It's an idiom, which explains why it can't be translated word for word.

In the U.S. it means "I gave up," "it was over," "I was finally defeated." In the literal meaning in boxing, when a boxer is knocked unconscious and falls to the floo, he is "down." The referee counts to ten. "the count" means "the full count of ten seconds." Perhaps the boxer is down for three seconds. Perhaps he is down for five seconds. If he is down for ten seconds, he is "down for the count" and loses. The game is over. A song sung by Jennifer Lopez begins: "I was down for the count Feeling like I've come to the end Nothing really mattered Nothing left for me to mend." She feels completely defeated. There's no hope of "winning," no hope of getting up, she feels as if her life were over. "But then you came... you healed me with your patience... I'm alive, I can breathe, I can feel, I believe... I'm awake, I survived." She was, as it were, able to "get up" and live again.

Someone or something that looks to be defeated, or nearly so. A term used in boxing, refers to a downed boxer who tries to get back to his feet before the ref counts to ten.

example: The grass in my backyard is turning yellow because I haven't been watering it regularly. I think the grass may be down for the count, but I'll try watering it to see if that helps.