The invention relates to a compressed-air supply system for operating a pneumatic installation in a pneumatic system of a vehicle, comprising: a compressed-air feed; a compressed-air connection point to the pneumatic installation; a venting connection point to the environment; a pneumatic main line between the compressed-air feed and the compressed-air connection point, which pneumatic main line has an air dryer; a venting valve, which is arranged on the pneumatic main line and is designed as a pilot valve and has a pilot connection point; a compressor having at least one compressor stage; and, in addition to the pneumatic main line, a pilot valve and a pneumatic pilot channel that connects the pilot valve to the pilot connection point of the venting valve. With respect to the compressed-air supply system, according to the invention, a pressure-holding pneumatic reservoir device is connected to the pilot connection point, which reservoir device is designed to provide a control pressure for the pilot connection point, in particular independently of a pressure in the pneumatic main line during venting of the pneumatic system, and the pressure-holding pneumatic reservoir device has at least one separate pilot pressure accumulator, which can be pneumatically connected to the pilot connection point via the control line.