Yes! The repetition of the word "mine" in "Mine, mine fair" is significant. In repeating the word, the persona reflects backward (to "that moment she was mine") and forward (to "mine fair,/ perfectly pure and good"). The backward reflection suggests his desire for ownership while the forward "mine" suggests a desire to possess a state of being (her fair, good, pure). By repeating the word, he tells us that it's not all about having her, but that it's also about preserving her perfect state--that moment of pure love for him.
That's the crux of his problem--he knows she loves him; it's just not enough.
He has told us already that although she loves him, she is not sufficiently committed to him. She wavers. He says she is too weak to follow her passion and to give herself to him forever (21-25). When he says she is "mine, mine fair", he is saying that he possesses her heart in its most perfect state. Were he to let her live, he would have her body sometimes, and her heart, sometimes, but...
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