I don't think it's possible for software of any kind to kill a battery. You can rule out battery problems IF your laptop goes to sleep when plugged into the charger. You can even remove the battery and compute.
This may be a long shot.. but there are network settings that automatically put a computer to sleep when a connection is dropped. Maybe something in the Wlan autoconfig is kicking in and causing a connection drop because it tries to find a better connection ever 60 seconds..... even if you aren't using a wireless connection.
I know this sounds pretty wild.. but I would put a book on my spacebar to make the computer think I was working and see if it still goes to sleep. If it doesn't go to sleep, then you know it's shutting down because it thinks Elvis has left the building.