A CMOS-based implementation of an autonomous Maxwell's demon was recently proposed [Phys. Rev. Lett. 129, 120602 (2022)0031-900710.1103/PhysRevLett.129.120602] to demonstrate that a Maxwell demon can still work at macroscopic scales, provided that its power supply is scaled appropriately. Here we first provide a full analytical characterization of the nonautonomous version of that model. We then study system-demon information flows within generic autonomous bipartite setups displaying a macroscopic limit. By doing so, we can study the thermodynamic efficiency of both the measurement and the feedback process performed by the demon. We find that the information flow is an intensive quantity and that, as a consequence, any Maxwell's demon is bound to stop working above a finite scale if all parameters but the scale are fixed. However, this can be prevented by appropriately scaling the thermodynamic forces. These general results are applied to the autonomous CMOS-based demon.