If you want to get the maximum life out of your batteries, you should not run them totally dead every time. But running them totally dead once in a while is totally fine. If you wanted to never run a 4AH battery down load, it wouldn't really be a 4AH battery anymore, would it?
In fact it's probably good for the batteries to run them down once in a while, maybe every 20 cycles or so. Less so with LiIon, but probably still not at all harmful.
What you do NOT want to do is to run the battery dead and then let it sit for months, because then self-discharge WILL run it down below critical voltage and you will damage the cells.