The Arc-AAA does not have rechargeable battery protection! The circuit in the Arc-AAA is like a vampire, it is designed to suck as much out of a battery as possible. This fits its design goal which is to be a light you can count on in an emergency. It will run down to about 0.15volts.
There is a video in the FAQ (should be) that shows how the Arc-AAA will produce a bright usable light for a decent amount of time on batteries that are so dead, other lights will not even light up at all. This is an important feature. The caveat is that this will also drain a rechargeable quite dead. Be careful.
If you use rechargeables, recharge the battery when it starts to noticably dim or after a month of use, which ever comes first. My father in law has been using a energizer NiMH in his for several years now with no problems.
Peter