RE: motor stopped working....
Not much info there, to really advice, as you tell us what heli (Century Swift) but not what motor, what pinion, or what ESC or what batteries (Brand, MAH and C rating).
The Swift heli is capable of taking the power of a system driven by a 4S, 5S or 6S packs, but that all depends what motor, pinion and ESC's are installed in it.
Yes, with many ESC's it is not recommended to fly at lower then 80% throttle settings. Doing so can cause overheating and damage components.
Also, when you went to a 6S pack, if you did not change pinions on your motor, you may have cause the rotor speed to increase too much. If so the much increased current draw may easily cause components to overheat enough to damage them.
Did you buy it new? If so the shop you bought it from should be able to help you.