I want to integrate a lithium ion charger into my circuit so I don't need a separate charger board, so it looked convenient to get a lithium ion charger with a built-in 3.1V LDO regulator to power my circuit from. The problem is that I want the regulator output to disconnect from my circuit when the battery voltage goes below its regulated 3.1V voltage, but none of the ICs I'm looking at appear to disconnect their regulator output when they can no longer supply the designated voltage. What's the best way to implement an automatic battery disconnect? I don't want to have to monitor the voltage using an ADC because I want to leave the microcontroller in sleep mode. Why don't regulators shut down when they can't provide their designated voltage anymore?
I'm open to other methods and ICs.
these are some of the chips I've found:
http://www.st.com/web/en/resource/technical/document/datasheet/DM00085223.pdf