low voltage battery disconnect from regulator
Why not you are going with a Switching regulator. Instead of LDO if you will go with the switching regulator, the backup for the device will be more since the efficiency of switching regulator is better than that of LDO's.

For example you can use TPS62240DDCRG4. This regulator has the provision of under-voltage lockout. If the voltage at enable pin is less than 1.85 Volt the device will be shutdown. In your case the regulator should shut down at 3.2V, so you can use a voltage divider at regulator Enable pin in such a way that when your battery voltage is 3.2V, the enable pin should sense a voltage of around 1.8V.