calvingloster:
So what am I to do? Must I just make sure I never use the battery until it gets that flat?
Yes.
At the very least you need to measure the battery voltage on the Arduino and go into a low-power mode when it reaches danger level (ie. shut down the laser, etc).
Even better is to power the entire system via a MOSFET and drive the MOSFET gate from a comparator so that the MOSFET shuts down when the comparator input reaches a certain voltage level.