We demonstrate the operation of a gain-saturated table-top soft x-ray laser at 100 Hz repetition rate. The laser generates an average power of 0.15 mW at λ=18.9 nm, the highest laser power reported to date from a sub-20-nm wavelength compact source. Picosecond laser pulses of 1.5 μJ energy were produced at λ=18.9 nm by amplification in a Mo plasma created by tailoring the temporal intensity profile of single pump pulses with 1 J energy produced by a diode-pumped chirped pulse amplification Yb:YAG laser. Lasing was also obtained in the 13.9 nm line of Ni-like Ag. These results increase by an order of magnitude the repetition rate of plasma-based soft x-ray lasers opening the path to milliwatt average power table-top lasers at sub-20 nm wavelengths.