It could be a number of things. Do you have a low voltage warning? Lipos aren't like nimihs where you just run them down until they die, they shouldn't be drained below 3.7 volts per cell. So in the case of your 4S, 14.8 volts.
What kind of charger are you using? A fully charged lipo should read 4.2 volts per cell. So your 4S should be 16.8 volts when fully charged.
Lastly, mismatched motor, props, gearing, calibration can cause too much current drain and too much strain on the battery. This is the most common cause of puffing but with your setup I doubt this is the problem. I must mention though, if you're using a cheap battery with a C rating of 30, this may be an inflated number. If it was in fact only 15 or 20, then yeah your battery may not be able to handle the power your motors are drawing.