If you're doing responsive design well, then you're showing appropriate layouts, images, and content for the dimensions of the device viewing the page. This doesn't mean shrinking everything for smaller devices.
Instead, it's most often necessary to server different layouts, different images, and sometimes different content for different devices. So the answer to your question is that you're serving the wrong content to smaller devices.
To fix that, I suggest using one of the following solutions:
- use a different image
- separate the image and the text so that you can scale the text separately from the image
- if appropriate, don't server the image, and serve formatted text instead.