Those reflective surfaces aren't perfect. Say that you have extraordinarily good ones, reflecting 99.9% of the light.(Ordinary mirrors would be about 100 times as absorbing as that.) After a few thousand bounces, almost all the light will be gone. If the room has typical dimensions of 3 meters, light bounces off the surfaces about 108 times per second. So in a few microseconds, the light is almost all absorbed.
Mike W.
(published on 12/19/2016)