Hi!
I have had same “battery deep discharge” problems on various gadgets. I solved some case with follow instructions:
Try to load you gadget to plug charger on and off multiple times. Everytime you plug charger to gadget some power goes to battery and then protection circuit is acting up. I think that reason is that there is no power and protection circuit is not working for that reason. When you plug on and off charger multiple time there is change that there is finally some power on battery and protection circuit come to life.
I use power timer for this. 1 min on and 1 min off..
