In the context of "... but either way, don't give up on yourself yet..."
Don't bury yourself?
Don't put a cross on yourself?
I'm not native so it's hard for me to decide if any of these even make sense in English
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There are a few phrases you could try, some work better than others depending on the exact (fuller) context you use them in and the person to whom you're speaking/writing. You might consider: