I have experimented and witnessed a new kind of crash. I left my character in Limsa Lominsa while playing in Windowed Mode, after around 5 minutes, I realized that nothing was moving. I clicked, and the game had been grayed out, and the "Not responding" message appeared in its brackets. The music was still playing, even when the game wasn't active (I do have the game set to mute the music when the game is minimised etc.). A simple click on the X to close it, did the job.

[Character names and chat were blurred for privacy]