Most like you hard coded an image path in your layout.master and the path is not correct in the other site or the image it refers to is not correct.
We have a convenience control built in to reference images in the skin folder without hard coding the path
<portal:SkinFolderImage id="myImage" runat="server" ImageFileName="myimage.png" />
The above is if the imager is in the skin folder iteself, if the image was in a subfolder named images belwo the skin folder then it would be like this:
<portal:SkinFolderImage id="myImage" runat="server" ImageFileName="images/myimage.png" />
This is helpful to make skins portable to another site by copying the entire skin folder. Copying only layout.master would not be sufficient since that doesn' include the image.
Hope that helps,