I can never win.
I can't ever win.
Can these be used interchangeably? Is there a case where one would work and the other wouldn't?
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Grammatically, they are absolutely interchangeable. Any advantage in one over the other would be a question of style.
In I can never win, the "n" in "never" stands for the negative "not". In I can't ever win, the "n't" in "can't" stands for the same negative "not". The effective statement in both formulas is the negative I can not win with "ever" modifying "win" as an adverb.
"never" is a simple statement of fact, whereas "not ever" says that it is a stronger command or statement.