Re: geometry disappears and reappears in render

This is the ever-present polygon battle that shows up in larger scale scenes in maya. The best way to tackle this issue is to really control your camera clipping planes. You can animate camera clipping planes so that you create the optimum distance, manually doing this is usually a lot better than the automatic scheme that maya will try doing at render time. As you're camera pulls away you can push the near clip plane farther away from the camera lense location without chopping your geometry off. You can also experiment with breaking your shot into layers so you can more rigourously set your clipping planes.

Another thing you can try to do is render double or quadruple resolution and scale down later, but that rarely works as well as grabbing the reigns on your clipping planes.