The dynamics of F(P-2(1/2))+H-2 scattering at ultracold temperatures is studied. It is shown that both the rotational and vibrational excitation of H-2 molecules decrease substantially the efficiency of spin-orbit relaxation in F+H-2 collisions. It is observed that the near-resonant electronic transition leading to rotational excitation of H-2(j=0) is of the same magnitude at high energies as the off-resonant transition in which the rotational angular momentum of H-2 is preserved but becomes dominant in ultracold collisions. The zero temperature rate constant for spin-orbit relaxation of F is computed and suggestions are made as to the chemical reactivity of F(P-2(1/2)) atoms at ultracold temperatures. It is found that rotational relaxation of excited H-2 molecules is significantly enhanced by electronic transitions in F atoms and the electronic relaxation in F(P-2(1/2))+H-2(j>0) collisions is suppressed by rotational relaxation of H-2.