First, optimize your catalog. File > Optimize Catalog
Try these optimization tips
If this doesn't work, then in my opinion this is most likely a memory issue. 4 GB is relatively small amount of memory these days, even though Adobe says it is sufficient. Most people do not experience "LR will run until it sucks up as much available memory as it can and then will drop dead." I have had computers with 8GB and 16GB of memory, and I have no similar problems.
It might also be that you need to you need to allocate more disk space to your camera raw cache, if you have the space on your hard disk. You should probably do this now.
Another problem that could cause this is a slow hard disk where your catalog and previews are stored (not the disk where the photos are stored).
The problem is NOT that you have 10,000 images in your catalog, which in my mind is a small catalog. It is not the size of the images nor is it the number of images displayed in the Library Module grid.