"Program stops"? It crashes?
And at only 1GB? Then it's not a 32bit limitation. As you said, it's way before the 32bit limit. Which normally is at around 2GB. With SU8M1 under a 64bit OS this is now 4GB - because they enable the large address aware flag.
Now, what is the size of the model you have? Faces, edges, groups components etc? The only time I ever ran into such memory usage has been when rendering with V-Ray. Without I have never ever ran into memory limitation with SketchUp. And then I've used models with 2million faces and lots of textures...