I've been able to alleviate some of my DX11 crashes by running the game in compatibility mode for Windows 7. The game still dies occasionally, but it's not constant like before. I don't know why or how this helps me, but maybe it will help you. It's ironic because the game will be dropping support for Windows 7 on January 14.

As a side note, really what is up with this game and DX11 lately? For me it all started around Patch 5.1. Judging by the number of posts in here, both from AMD and NVIDIA owners, all clues point to an issue with the game itself and not user error. I really hope someone can communicate something to the Dev team because it's very frustrating to new and old players alike.