  The radiation reaction in compact spinning binaries on eccentric orbits due
to the quadrupole-monopole interaction is studied. This contribution is of
second post-Newtonian order. As result of the precession of spins the magnitude
$L$ of the orbital angular momentum is not conserved. Therefore a proper
characterization of the perturbed radial motion is provided by the energy $E$
and angular average $\bar{L}$. As powerful computing tools, the generalized
true and eccentric anomaly parametrizations are introduced. Then the secular
losses in energy and magnitude of orbital angular momentum together with the
secular evolution of the relative orientations of the orbital angular momentum
and spins are found for eccentric orbits by use of the residue theorem. The
circular orbit limit of the energy loss agrees with Poisson's earlier result.
