The interaction of ultrashort laser pulses with opaque droplets in the atmosphere is examined numerically. Intense filaments resulting from the balance between self-focusing and ionization of air molecules are shown to be robust against obscurants sized up to 2/3 of the filament diameter. (3D+1)-dimensional numerical simulations confirm recent experimental data [F. Courvoisier et al., Appl. Phys. Lett. 83, 213 (2003)]. The filament is rapidly rebuilt with minimal loss of energy over a few cm after the interaction region. The replenishment of the pulse mainly proceeds from the nonlinear attractor responsible for the formation of a spatial soliton modeling the filament core.