諦めるな = Don't give up 諦めはしない = I (He or She) won't give up Thumbs up Masaya!

I think whichever is OK . It depends on the place that it is used.

I think it's because that type of subject in Japanese is more often omitted. But in English, they don't usually omit the word like I, you, he and she etc, so the translator intentionally added “I” Without the “I”, It's probably hard to understand who said it, or in Japanese, “Don't give up” could be 諦めるな. In fact, 諦めるな and 諦めはしない are different in meaning. 諦めるな is imperative and 諦めはしない means like the speaker's or someone's intention.