1
general::
Defeated, finished, doomed, as in I doubt if he'll ever leave the hospital; his illness really has him down for the count. This expression alludes to the losing boxer, unable to get to his feet before the umpire has counted to ten (the count). [1920s]
American Heritage Idioms
2
general::
Phrase(s): *down for the count 1. [and] *out for the count
[of a boxer] knocked down by an opponent’s punching and remaining down until the last count, or even beyond. (*Typically: be ~; go ~.) • Wally is down for the count. Chris is the winner. 2. eliminated from something or an activity for a period of time, perhaps permanently. (*Typically: be ~; go ~.) • I can’t continue with this course. I’m down for the count. • I’m down for the count. I have the flu.
McGrawhill's American Idioms And Phrasal Verbs