Classically you have been given references in the other answer. After all the black body simulation as a cavity filled with photons assumes total reflection.
Mirrors and reflections though, when one is talking of limits, as is the case of total reflection, are quantum mechanical objects.
Quantum mechanics means
a) that the Heisenberg uncertainty principle holds .This means that there is always a width of acceptable angles
b)that reflections are the quantum mechanical solution of the electromagnetic interaction with the electrons on the shells of the mirror. By nature, when one has an interaction at the quantum mechanical level there is always a partial solution giving other results than total reflection. These will be with very low probability, but considering you are thinking of trapping light for at least 24 hours this means there are zillions of interactions and then the absorption probability adds up.
So it all depends on probabilities and time constants. My calculation tools are rusty but I guess that even with a clever focusing device the photons would be absorbed within nanoseconds, raising the temperature of the walls of your cavity.