Another player was having a similar issue when closing out of ESO. We've posted troubleshooting in the thread linked below that may help in your situation.
Oh! that explains why i was sure i clicked "logout" yesterday and yet the game still closed without any error or crash prompt. i thought i maybe clicked quit instead... but after rewatching shadowplay i clicked "logout" as well.
I started to have the same problem a few weeks ago. But I think I found the culprit. If you have Razer Synapse, try disabling support for ESO in the Chroma Apps tab. You may need to install the Chroma Connect module first.