I have 8 NiMH AA batteries in series, and they have a different discharge rate (even though they are new batteries), therefore having some batteries going on the negative side, while others are still 1.2 Volts.

What can I do to protect each battery to discharge below a certain voltage, like 0.9 Volts (edit, 1 Volt) ?

 

Never discharge below 1V/cell unless you know what you are doing, such as in a battery analyzer, where you can go to 0.7V/cell individually to revive them.

If they've gone negative, revival is usually not possible.

I'd add a cutoff circuit for 0.9V/cell in the electronics, and a low battery warning at 1V/cell

 

OK, 1 volt then... I edited my first post.

The question remains... what to do (schematic ?) to prevent from over discharging?

 

Often a Zener diode to turn on a MOSFET transistor to allow current. When the Zener hits the cutoff point, a high value (1M-ish) resistor in parallel with the Zener will discharge the MOSFET gate and turn the MOSFET (which allows all current to the rest of the circuit) off.

Do a search for low voltage cutoff circuits and you'll find many.

 

OK, 1 volt then... I edited my first post.

The question remains... what to do (schematic ?) to prevent from over discharging?

A controller that monitors each cell voltage and disconnects the load when any of the cells is depleted.