Actually the default TwentyThirteen header image does the same thing, it gets cropped on the left and right when you make the browser narrower. It’s just not that noticeable when you resize the browser because the site title and tag line is actually text and not part of the header image like yours is. You’ll see that this is a common complaint on the TwentyThirteen support page.
I’ve come up with a solution here, if you want to give it a try. It shouldn’t be too difficult for you since you’ve already created a child theme.