What happens a lot of times is that if you watch HB's log, you will see your toon is trying to "Move to Vendor" in order to repair and sell items, however whenever they try to go back to their corpse, the mob in the area will kill them again since they have no armor/weapons to use because their durabilities are at 0. In this case you most likely need to manually get your body and then get to a clear area and start running HB again. This has happened to my rogue many times.
As far as hearthing, what exactly are you looking for? The AutoLogOut plugin utilizes the hearthstone at a certain level to log you out.