Increasing the protein production capacity of the PURE cell-free transcription-translation (TX-TL) system will be key to implementing complex synthetic biological circuits, and to establishing a fully self-regenerating system as a basis for the development of a synthetic cell. Under steady-state conditions, the protein synthesis capacity of the PURE system is likely at least one order of magnitude too low to express sufficient quantities of all PURE protein components. This is in part due to the fact that protein synthesis cannot be sustained during the entire dilution cycle, especially at low dilution rates. We developed a microfluidic chemostat augmented with semipermeable membranes that combines steady-state reactions and continuous dialysis as a possible solution to enhance protein synthesis at steady-state. In batch operation, the continuous dialysis of low molecular weight components via the membranes extended protein synthesis by over an order of magnitude from 2 h to over 30 h, leading to a 7-fold increase in protein yield. In chemostat operation, continuous dialysis enabled sustained protein synthesis during the entire dilution cycle even for low dilution rates, leading to 6-fold higher protein levels at steady state. The possibility to combine and independently manipulate continuous dialysis and chemostat operation renders our dialysis chemostat a promising technological basis for complex cell-free synthetic biology applications that require enhanced protein synthesis capacity.