Geosynthetics are increasingly used in geotechnical engineering to replace conventional solutions due to their cost-effective and environmental benefits. For example, geotextiles can be used in sustainable waste-dewatering systems to confine solid waste for final disposal. This study is presented to analyze the durability of a geotextile regarding cyclic fatigue induced during the pumping stages in these sustainable waste-dewatering systems. A polypropylene woven geotextile was used and subjected to cyclic tensile loading levels of 10%, 30% and 50% of the ultimate average tensile strength. We also used hysteresis loops with a frequency of 0.1 Hz at different numbers of cycles (10, 20, 30, and 90 cycles). With a 95% confidence level and response surface, the results show that increasing the tensile loading levels and the number of cycles made the geotextile lose its tensile strength. Laboratory experiments simulated scenarios where the geotextile was subjected to cyclic fatigue that might directly impact its strength–strain and hysteretic stiffness performance over its design lifetime. This study contributes to a better understanding of the durability of geotextiles to subsidize decision-making involving social, environmental, and technical impacts in waste-dewatering system applications.