I have an ad that looks fine when the web page is at 100%, but when the user changes the screen size, my responsive design takes over and while the image is still correct looking, the text has reduced to a size that is almost unreadable.
Is there a font where even when reduced inside an image that is still relatively easy to read?
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:
If the text is being rendered smaller than 7-9 pixels high, it will make just about any font illegible. As there simply isn't enough space to fit the shapes within the pixel grid.
If you can serve a vector based version of the text, either as a SVG file or using HTML. You can then control the size of the font independently of the image.
Alternatively you could serve two versions of images to different resolution screens, using a media query.
