The first thiing that comes to my mind is a resources issue. As you have a stout computer, with more than adequate RAM, unless something is failing (like a stick of RAM), or perhaps the GPU, I would not expect to see what you observe. On a much less powerful machine, I have no problem running PrPro, Encore, Photoshop, Illustrator, and a word processor, all at the same time.
I would look into this ARTICLE, which starts with some general tips on setting up one's computer for running PrE, and then goes into system and OS tune-up tips (this is probably where I would start, if the intitial checklist looks OK), and then goes into troubleshooting. I would definitely look here, and especially using Event Viewer to try and track down what is happening, when the crashes occur, and also the one on tools to test RAM, GPU's, etc.).