I render my sky box with a separate camera with a field of view of 60 degrees. The rest of the game is rendered with a separate camera with a variable field of view with can be as low as 2 degrees.
The problem is that the amount of rotation needed make the sky box matchup with the lower field of view camera's rotation is different. For example say you want to aim at a cloud with mouse look. The amount of rotation you need to apply to the skybox camera is not equivalent to the amount applied to the camera with the lower FOV.