  We present resistivity and magnetization measurements on proton-irradiated
crystals demonstrating that the superconducting state in the doped topological
superconductor Nb$_x$Bi$_2$Se$_3$ (x = 0.25) is surprisingly robust against
disorder-induced electron scattering. The superconducting transition
temperature $T_c$ decreases without indication of saturation with increasing
defect concentration, and the corresponding scattering rates far surpass
expectations based on conventional theory. The low-temperature variation of the
London penetration depth $\Delta\lambda(T)$ follows a power law
($\Delta\lambda(T)\sim T^2$) indicating the presence of symmetry-protected
point nodes. Our results are consistent with the proposed robust nematic $E_u$
pairing state in this material.
