Have you ever moved the location of the Plex data folder away from its default?
If that drive has changed its drive letter, or is no longer present, or the folder Plex has been told to use has been renamed or removed, Plex server will close itself immediately again.
Take a look into the Windows registry to see if that is the case.
The branch of the registry is named here: [HowTo] An extended guide on how to move the Plex data folder on Windows
