Images disappearing in component instance when I toggle between properties

I created a main component that has two variants: one for desktop and one for mobile. When I pull an instance of that component into a linked file and insert an image into the component in the desktop variant, the image goes away when I toggle to mobile - just reverting back to the mobile component. What I want is for the uploaded image to remain and just to to resize when I toggle between desktop and mobile. How can I do this?