We introduce a versatile high-repetition-rate solid tape target system suitable for relativistic laser-plasma driven secondary sources. We demonstrate the operation and stability monitoring based on a petawatt laser focused at 1 Hz. Experiments were carried out at the VEGA-3 laser system of the Centro de Láseres Pulsados facility where results for different tape materials and thicknesses are presented. Experimental proton spectra were recorded by a Thomson parabola spectrometer and a time-of-flight detector. In addition, non-invasive detectors, such as a target charging monitor and ionization chamber detectors, were tested as metrology for the stability of the source. Degradation of the proton signal at high-repetition-rate operation was observed and it was solved by online optimization of the relative focus position of the target and laser beam parameters. We report the use of the tape target for bursts of 1000 shots at 1 Hz with mean cut-off energies of about 10 MeV in optimized interaction conditions.