We present a compact closed-loop recycling system for noble and inert gases. It has been developed for an extreme-ultraviolet (XUV) frequency comb based on high-harmonic generation at 100 MHz repetition rate. The system collects gas injected at several bars of backing pressure through a micrometer-sized nozzle into the laser-interaction region with a differential pumping system comprising turbomolecular pumps, and subsequently compresses the gas to a pressure of up to 200 bar. By drastically reducing the waste of expensive gases such as xenon and krypton, it enables the long operation times needed for spectroscopic measurements, as well as for continuous operation of the XUV frequency comb.