I Reset() the device if F4 is pressed, toggling the fullscreen.
All my resources are loaded with the managed pool. I know vertex data is preserved, because meshes are still appearing with the correct shape, but for some reason, textures are disappearing. This only seems to happen when I load up a cube texture at the start of the game - without the skybox, other textures are restored correctly when fullscreen is toggled.
Solved. It was actually the DRAWING of the skybox that was causing problems. (Setting some shader constants which weren't reset for drawing meshes, making them appear black, which tricked me into thinking the textures were being lost).