Due to their unique properties such as transparency, tunability, nonlinearity, and dispersion flexibility, liquid-core fibers represent an important approach for future coherent mid-infrared light sources. However, the damage thresholds of these fibers are largely unexplored. Here we report on the generation of soliton-based supercontinua in carbon disulfide (CS2) liquid-core fibers at average power levels as high as 0.5 W operating stably for a long term (>70 h) without any kind of degradation or damage. Additionally, we also show stable high-power pulse transmission through liquid-core fibers exceeding 1 W of output average power for both CS2 and tetrachloroethylene as core materials.