The trick is that, if you ignore the thermodynamics of information processing, Maxwell's demon can work with arbitrarily little energy (the only physical work it is doing is opening/closing a door with arbitrarily little mass). In fact Maxwell's demon can perform any amount of thermodynamic work with essentially zero physical work. It really does seem to be a violation of energy conservation.
The only way to solve this is by considering the thermodynamics of Maxwell's demon's brain (creating and destroying state as it determines whether or not to let a given molecule pass the door) - and in particular understanding that there is a fundamental thermodynamic cost to storing or deleting information, it is not just a consequence of imperfect circuit/neuron design.