Is there a way to get around this problem?
Blender Cycles and Blender Internal are two completely independent rendering systems with different settings and material definitions.
Your UV Maps did not disappear, you just have to recreate your materials using the Cycles material nodes system.
Have in mind that even after recreating them, the Blender viewport does not support displaying material previews for cycles, only basic preview of image based textures, so you will only get to see them upon rendering or on interactive viewport render.
UV Maps don't disappear. What's happening is that Blender Internal Shaders are very different from Cycles shaders. So if you switch from BI to Cycles, you have to set up your shaders for cycles. They're not converted automatically. For a simple diffuse shader with your image texture, you'd first need to press the Use Nodes button, since Cycles materials are node based. A diffuse shader will be created by default. Then for the color input there's a little icon to the right. Click it and select image texture. Select your image, and for the vector input select UV (under texture coordinate). That will give you a basic cycles shader setup that will render your image texture using your uv map.