Grammar-monster defines “dead in the water” as a nautical term meaning to have no momentum or chance of progression.
Answers.yahoo doesn’t find the origin either, calling it a colloquialism.
Good old Phrase Finder offers “all the pre-1829 citations I can find of that phrase are literal references to things (fish etc.) that are in the water and dead,” but doesn’t mention the first metaphorical use.
The site diverted me to a phrase with a more explicit origin. The term “dead duck” is called an “old saying” but first found printed in the New York Courier in June, 1829:
“There is an old saying ‘never waste powder on a dead duck’; but we cannot avoid flashing away a few grains upon an old friend, Henry Clay.”