Jim -

If your 3S lipo is only "over 11 volts at full charge" that could be the problem right there.

A 3S lipo at full charge should measure 12.6V. Full charge for any lipo is 4.2V per cell.

If your "fully charged" lipo is much less than 12.6V, there is a problem with either the battery or with your lipo charger.

On the other point, yes, if a battery is too small for the job, its voltage may drop so much that the ESC cuts off the motor.

- Jeff