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BQ2970: When Battery voltage is < Underlockout voltage, BQ25101 doesn't charge it

Part Number: BQ2970
Other Parts Discussed in Thread: BQ25101,

 Hello,

I have a circuit composed of a BQ25101 Lipo Charger with I_OUT set to 10mA and a BQ29700 protection chip.
This circuit is made to have a very low power consumption and board size.

When Battery is above 2.8V, it's working well, charger could charge it at 10mA, board is working.

But when battery is below 2.8V, over-discharge protection comes in and even with charger connected, it doesn't work. 
Voltage between BAT and GND is 1.3V 
Current sunk from power supply is 2.7mA (the rest of the board is under 500uA)

I have no idea what the problem could be.
Please tell me if more information is needed.

Thanks for your help