Yes, if you Pause the session it will keep it open, even if you turn it off, and you can Resume it once you turn it back on. If you don't, the session is closed when you turn it off (or it turns itself off, apparently). I have not had one time-out on me yet, I didn't know they would even do that. So, it turned off after a certain length of time with no activity? Does anyone know how long before it does that?
With several updates to the software already, and quite a few complaints that were registered that I'm aware of, it sure seems like that would be an easy fix for them to incorporate: Just allow any session to be re-opened.