I have the instruction sheets for two different models (6" & 24") in front of me. They both say that ABS is used to "Set increment (INC) (relative) zero". I think it stands for Absolute.
Mine shut off the display if there hasn't been any movement in that axis for several minutes. When you turn it back on, it will read accurately, even if you moved it while it was dark. The battery is actually holding information and even calculating all the time. Just the display is turned On and Off.
One issue I've noticed on one of mine is that the display will sometimes scramble if there is a lot of vibration where the display module is mounted. Turns out it was due to a loose connector where the wire plugs into the display. I unplugged nit and put a twist in the wire between the little clamp and the connector and plugged it in again. That seems to have fixed it.