Thanks Richards,

Sorry, maybe the word "trip" is not adequate (I'm speaking french)

BTW, what would be the correct word: "latching"?

I found this interresting video which made me start to try battery monitoring:

.

Unlike the video, I started with a 2 resistors divider. But a potentiometer (maybe easier for a start) and a corrected register CM2CON0 as you suggested made it work.

So, I missed this one you kindly pointed me to:
Name: 000246.png Views: 4222 Size: 7.9 KB

Finally, the "shortest possible" working code for a 0.6Volt threshold detection could be:
Code:
TRISC      = %00001000 ' Comparator's input port

CM2CON0    = %10100111
' Bit7     = comparator 2 is ON
' Bit5     = comparator's output pin (i.e. LED) is PORTC.4 (for "proof of life")
' Bit2     = connect Vref to C2Vin+
' Bits1:0  = comparator's input pin (i.e. Vbatt) is PORTC.3