Nanoantennas made of high-index semiconductors with a strong nonlinearity and supported optical Mie-type resonances offer a promising alternative platform for nonlinear nanophotonics. In this Letter, we employ an array of amorphous silicon nanodisks with varying diameters to produce a broadband deep-ultraviolet third harmonic of a few-cycle Ti:sapphire oscillator. Ultrashort light pulses efficiently deposit their energy at the center of the disks where the electric field is strongly amplified by the anapole states. This leads to a progressive material modification in an extreme multishot (>1010 pulses) and a rather low fluence (<10-3 J/cm2) regime, drastically differing from other known mechanisms, such as nonthermal plasma annealing or thermal melting-induced recrystallization. We suggest that the material modification is due to femtosecond laser-induced excitation of dangling bonds, which leads to a gradual boosting of the third harmonic conversion efficiency and broadening of its spectral bandwidth.