A couple of options for consideration

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Note added at 1 hr (2022-10-21 13:39:16 GMT)
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I think the more formal "do not" (rather than "don't") aligns much better with the style and register of the text

Spanish term (edited): no se me rindan

- as in the Crucifixion vs. Do not give up my Ghost that is the name of the song with unfortunate self-harming overtines,

rindan: third-person plural imperative of rendir, Verbos españoles, Payot, Lausanne, CH.

Don't give up (on my watch).

In this particular case, it would be more natural to use a positive. As others have noted, the use of "me" is only a "dativo de interés", since it wouldn't be "don't give up on me" but rather "don't give up on God".

I proposed we take ten young people to walk the streets of Kolkata ... but God wants you to keep pressing ahead, pursuing ventures that will ...
https://www.brighthope.org/blog-stories/serving-the-poor/ste...

Keep moving on in the presence of God. Ask God to help you get through the responsibilities of the day and to experience his presence and strength as you do ...
https://www.pursuegod.org/going-deep-with-god-in-depression/

10. Why is it important to keep moving on, despite if others try to discourage you from doing what you believe God wants you to do?
https://www.northvalley.org/download/2898

Keep moving ahead! ... Do not let other people frame boundaries for you. ... Be yourself and believe in God who already believes in you.
https://www.sundaymail.co.zw/keep-moving-ahead

Spanish term (edited): No se me rindan

Short and sweet, and seems fitting.
Another one that occurred to me was "rest assured of that", but that might be a bit of an over-translation.

Spanish term (edited): no se me rindan

Pienso que el dativo ético "me" de énfasis en español se puede reemplazar con "just", que igualmente puede ser enfático, como indica el Diccionario de Cambridge:

"Just" for emphasis:
We also use just to emphasise an imperative:
Just shut the door quickly or we’re going to be late.
https://dictionary.cambridge.org/grammar/british-grammar/jus...
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Ejemplos:
Ejemplos:
My main reason to write this is to say to anyone who is considering suicide or feeling that they may have depression then please, just do not give up.
https://www.alustforlife.com/voice/personal-stories/if-you-a...

Be prepared to fail, just do not give up. Keep working on your passion, keep trying, because that is the only way you will be able to ...
https://purposefocuscommitment.com/mindset-story-while-one-g...

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Note added at 9 hrs (2022-10-21 21:44:38 GMT)
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Ejemplo de uso en español y en inglés:
Mi hijo no me come = Literally: My child does not eat me = My child just does not eat

MI HIJO NO ME COME:
¡Socorro: mi hijo no me come! Ahora, cada vez que le toca comer, es una pesadilla. El niño se niega a comer nada de lo que le ofrezco y me ...
https://www.nestlebebe.es/articulo/socorro-mi-hijo-no-come

MY CHILD JUST DOES NOT EAT:
"My child just does not eat and is very thin"-This is a common woe of you like many other parents most of the times. What you need to know...
https://www.parentlane.com/child/child-development/choosy-ab...

...from the path of righteousness, or similar;