  We study the out-of-equilibrium dynamics of a BCS superconductor in the
presence of a periodic drive with a frequency $\omega_d$ larger than the
equilibrium superconducting gap and an external bath providing dissipation.
Similar to the dissipationless case, a subset of quasiparticles, resonant with
the drive, synchronizes and produces interesting non-linear phenomena. For
small dissipation Rabi-Higgs oscillations [Collado et al. Phys. Rev. B 98,
214519 (2018)] can be observed as a transient effect. At long-times in
contrast, dissipation leads to a steady state with a population imbalance that
increases quadratically for small drives and saturates for large drives as in
non-linear quantum optics. We show also that second harmonic generation is
allowed for a drive which acts on the BCS coupling constant. We also compute
the intensity of time- and angle-resolved photo-emission spectroscopy
(tr-ARPES) and time-resolved tunneling spectra. The excited quasiparticle
population appears as a decrease (increase) in the photo-emission intensity at
energy $-\omega_d/2$ ($+\omega_d/2$) measured from the chemical potential. The
tunneling intensity shows a time-dependent depression at $\pm\omega_d/2$ due to
the lacking of spectral density and population unbalance causing Pauli
blockade. We predict that at short times, compared to the energy relaxation
time, both experiments will show oscillations with the Rabi-Higgs frequency.
