I have the exact same issue. I've tried everything from uninstalls and clean installs of drivers, removing all my peripheral devices and reinstalling them. Nothing has worked so far. My issue started the night of Heavensward's release but it's always in Limsa's Aftcastle, the second boss of the Aetherochemical Research Facility and a few random spots in the beginning of said dungeon. DX9 never gives me an issue, I've tested it and it works perfectly, it's something with DX11[currently sitting in the Aftcastle in DX9 with no issue after being kicked every load-in with DX11 for the past 3 hours].

My specs are an NVIDIA GeForce GTX 970 gpu, Intel i5-4690K cpu, and Windows 8.1.