The electrons of the mirror interact with the incoming photon and emit a photon in response. It is not necessarily exactly the same (e.g. change in polarization). The process is typically not 100% efficient, hence no perfect reflection.
But again conduction is typically not 100% efficient unless you get super-conduction. So a maybe a material analogous to a superconductor could be used. A superconducting mirror may not be 100% efficient but the waste heat cold be readily shunted to better preserve the mirror.
Remember high-temperature super-conductors were once handwavium, they had to come up with a theory just to explain them. So be not detered.
I seem to recall some weird properties of the Bose-Einstein condensate that might help as well. Maybe Google that.
A monopole may also be able to deflect, if not reflect, light. The predicted interaction of the monopole with light is two or more orders of magnitude stronger than for electrons. Since we don't see monopoles in nature (or at least yet) they probaly have a very, very small lifetime (if they exist). However, some form of advanced energetic field may be used to keep them "alive" to serve as your shield.
