This paper investigates robustness of finite-time stability property for a homogeneous nonlinear dynamical system with sufficiently small affine inputs. In addition, robust stability conditions are presented for the systems admitting homogeneous approximations at the origin or at infinity. The effects of additional stable unmodeled dynamics in the input channel on robust stability are investigated. The utility of the obtained results is illustrated via robustness analysis of homogeneous observer with time-varying gains.