First of all, green led on the ESC is on, correct? Second, if you bothered to read the manual, both ESC's have a 3V cut off (which is too low IMO) which is setup when you choose lipo mode.

So a 3S will cutoff @ 9V, a 2S @ 6V. If you installed this "balance buzzer" (low voltage alarm?) and it fell off, how is that the ESC's fault? And at what voltage is it supposed to go off? And if one lipo's cell dropped to 2.5V and the other(s) is 3V or above, then that pack is obviously not in good shape.