Excellent question. Any potential differences would be subtle and nuanced. First, I suppose they COULD sometimes mean the same thing.
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pructusb. I don't want to give up on you.This could be said about your son, who has failed time and time again. But you still support him, having faith that he will succeed eventually.
pructusa. I don't want to give you up.Your son has been caught on camera doing drugs. He is in the bedroom, and the police are at the door.