Wildest guess in the world: you have a long cable run (10 feet) from the battery to the inverter, coupled with a small gauge wire (12 instead of 10, leading to a voltage drop (barely 12.1 at the inverter, instead of 12.7). So when you hook a 100 watt device to your 400 watt inverter, the low voltage alarm goes off. with a reading of 11 volts.
More details would help narrow down the issue!
2012 Fun Finder X-139 "Boondock Style" (axle-flipped and extra insulation)
2013 Toyota Tacoma Off-Road (semi-beefy tires and components)