Hi Sankalp, for photobleaching you need light. If you keep you samples in the dark, then it is not photobleaching that you are observing. However, a general strategy for reducing photobleaching is to keep the oxygen concentration in your samples as low as possible.
A short-term solution is to add an enzymatic oxygen scavenging system, like glucose-oxidase/catalase. But this will only work on the minutes timescale and not at a temperature of -80 C. Otherwise, you can consider storing your samples in liquid nitrogen, but I don't think these suggestions will solve your problems, as light is required for photobleaching.
As Guus said, you shouldn't have any photobleaching problems if you keep your samples in the dark. Chemical stability of your sample is a different issue, but in general you should be OK at -80. What I would recommend is to split your sample in a series of aliquots, so you don't have to thaw all your stock solution each time you do an experiment.