I got the following response from Woothemes:
“I’d recommend adding the header image as the Custom Logo via Settings – this will make the image responsive. There’s no perfect solution for a responsive image when adding it using css ( background image)”.
I then asked the following question: Does this mean that if I want to add a logo that I’ll have make it part of the header image?
Yes, this is one option, or you can customize the header.php file and add the logo directly there.
Though customizing the header.php is beyond me, I hope this helps other people.