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Laser-driven proton accelerators are relevant candidates for many applications such as material science or medicine. Today, there are multi-hundred-TW table-top laser systems that can generate relativistic peak intensities >1018 W/cm2 and routinely reach proton energies in the MeV range. However, for most desired applications, there is still a need to optimize the quality and stability of the laser-generated proton beam. In this work, we developed a 0.625 Hz high repetition-rate setup in which a laser with 2.5% RMS energy stability is irradiating a solid target with an intensity of 1019 to 1020 W/cm2 to explore proton energy and yield variations, both with high shot statistics (up to about 400 laser shots) and using different interaction targets. Investigating the above-mentioned parameters is important for applications that rely on specific parts of the proton spectrum or a high ion flux produced over quick multi-shot irradiation. We demonstrate that the use of a stable "multi-shot mode" allows improving applications, e.g., in the detection of trace elements using laser-driven particle-induced x-ray emission., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)