Why do photons keep their polarization when they reflect? I understand that photons do not change their polarization when they pass through glass because they are not absorbed in the glass due to the band gap. 
I also now understand that reflection does not involve the absorption of re-emission of a photon, although I am somewhat unclear at the quantum level what is happening in reflection. It is clear to me that the object reflecting the photon (like a solar sail) slightly increases in momentum,  and since momentum is conserved, the photon must have a slight decrease in momentum, which means that the photon must decrease in frequency somewhat upon reflection.
So my question is why does polarization not change on reflection. Is this because it's the same photon (whatever that means), so there is no opportunity for its quantum state to change, even though it's momentum vector has changed?
 A: The answer is that the polarization does change upon reflection unless the medium it reflects off is a perfect metal. Only for perpendicular incidence the polarization remains the same, although effectively right and left turning circular polarization transform into each other as the propagation reverses. For all other angles the reflectivity and transitivity depend on polarization. At the Brewster angle of incidence only TE polarization is reflected. Polaroid shades use this effect to suppress reflected light.
A: At the quantum level the photon is indeed absorbed and re-emitted ("scattered") all the time in the materials including the mirror. The resulting macroscopic propagation is the result after all the quantum amplitudes of all the scatterings and propagations interferences are summed up.. For practical purposes the classical optics wave description of light reflection works fine, but I guess you ask about the underlying action :) 
In either case, polarization might not depend on the linear momentum change but angular momentum can be transferred to the reflecting object, thus changing polarization of the reflecting photon (see "optical torque").
