I’m running an Openfire server on a Windows server 2012. After a Windows update and restart, the Openfire server stops when I log off of my Remote Desktop session. If I leave the session open, Openfire stays up. I don’t see anything in the event viewer.
If you are using it via the Launcher, then it is normal that all simple user applications (which a Launcher is) quit when you log off a user session. You should install it as a service. Unless you already have. Then it is another issue.
Windows Service Openfire: Installation Guide