Hi, it’s little bit more complex.
For AAA Alkaline or NiMh battery cell you can follow this rule: When the battery voltage is is under 1.2 V it is almost empty (good time to replace it). When battery voltage is under 1.0 V it it is completely dead. And it is nod good condition for some types of Alkaline cells (like Duracell, Varta is better), it can cause electrolyte leak.
About minimal voltage for BigClown Modules using Mini Battery and Battery Modules:
Mini Battery Module (2 x AA) is equipped with Step Up regulator, regulating output voltage to 3.1V When the voltage of two AAA batteries falls under this voltage, it can still boost it to 3.1V and all modules will works fine. Theoretically the minimum input voltage is 0.7 V (0.35 V per cell ). But when the battery cell has les than 1.0 V the voltage falls very rapidly after load.
Battery Module (4 x AAA) is equipped with Step Down regulator regulating output voltage to 3.1 V. When the voltage is less than 3.2V (0.8 V per cell) the regulator disconnect the output. It matches your comment.
In booth cases Battery or Mini Battery module, battery cells under 1.0 V is not stable condition, and it can cause for example reset of MCU during measuring CO2 or turning on LED on Core module