Sounds like some other process/application is locking one or more files/processes that FFXIV uses for some reason, thus not allowing it to close in a timely manner. I'll assume you're not using any 3rd party mods so Anti-virus maybe? Or something to do with Direct X/Graphics Drivers? Just an off-the-top-of-my-head thought on it based on similar issues I've seen with other applications in the past.