I'm not sure if Lithium Ion battery chemistry has changed, but it's always been my understanding that it is not good to let a Lith-ion battery become fully discharged. If I saw that my battery was getting really low, I would turn the phone off until I could get it on the charger.
The way i use mine, it typically has about 60% battery left at the end of the day, so I just put it on the charger, then put it on in the morning. It asks me to sign in at that time, but I do not think it has been off, just locked.