Leupold can adjust your scope to be parallax free at a specified distance. You can also do this yourself if you're so inclined - several DIY guides on YouTube. Personally, I don't think it's a problem for rabbit shooting etc. Even if you've got your head out of alignment with the scope and can observe some small amount of parallax, you'll probably still be in the kill zone on your target.
As others have said, the odd flyer won't be due to the scope.
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