the aspiration

Use this sentence:

He had lost all the aspiration to fight even before the battle began.

How about this one:

...and losing all the aspiration, her gaze became morose.

AskAndAnswer...and losing all the aspiration, her gaze became morose.

That is what grammarians call a "dangling modifier."

...and losing all the aspiration, her gaze became morose.

I see, so changing "the" to "her" would work in this case. Correct?

...and losing all her aspiration, her gaze became morose.

But then the "her" sounds repetitive a bit.

Her gaze did not lose all aspiration.
The problem is that the modifier (losing all aspiration) does not modify the subject (gaze).

I should have had a more complete sentence to give. I mislead you I believe into thinking the subject is gaze.

The queen collapsed, and while losing all her aspiration, her gaze became morose.

Does that work?

Yes, grammatically speaking, that converts the present participle (losing), to a gerund (object of the preposition "while").

Aspiration should be plural here. Usually these things don't come in ones, they come in multitudes.
It is different from the word "hope."