Rotating camera clips my objects

When I tip my camera up/down, if an object's center point goes off the edge of the screen, the entire object is not rendered at all, causing instant clipping from view. This looks DREADFUL! Is there any way to make the object render all the way to the edges, or at the very least always render? (particularly in players, but ALL objects would be nice)

If you need to see what I am talking about, I can make a small video. Just let me know.