That's not entirely accurate. It will take a 6A charge no matter what level the battery is at. The problem is how you are calibrating/tuning the cc/cv. You need to use something other than one of the batteries to tune it to 6A, because as soon as you hook the battery up to it the battery starts charging making your 6A a moving target since the amperage starts to immediately drop. You need to put a dummy/constant load on the cc/cv when tuning. Something that will pull more than 6A, like a car battery or dummy load. Once I did that and got them perfectly dialed in to 6a/16.8v, they charged the batteries no matter what level they were at and never power cycled again.
Here are some charts I made using actual battery data coming of the smbus when charging. It shows the amps dropping off (move your mouse over the lines to see the readings) as the battery charges. Look in the lower right part of the screen for the graphs.
Charging 3DR Solo Batteries - JSFiddle
The battery draws the most amps when completely discharged and it curves down from there as it's charging. So if you try to calibrate the charger for 6A on a battery that isn't completely discharged you are setting it wrong because when you try to charge the same battery at 10%, the cc/cv will be putting out more than 6A which will cause the power cycling.