No. There is no such thing as perfect mirror and the fact that somebody is observing what is happening inside the box means that he or she absorbs photons (e.g. with eye cells, for example: rod cells are very good at that, as they can detect a single photon with 25% probability, but they absorb it during the process). Candle will also absorb energy of light.
Please do notice that You asked:
"MY QUESTION IS if there is no energy loss then whether the observer could see the light or not?"
That doesn't mean that there is no transformation of energy. So in that case, energy of light will be transformed to heat.
If we suppose that there is no energy transformation the light would be there forever or untill the box is oppened or decays or something like that. However this is only mind experiment and it cannot be done (light is usually very fast and boxes are relatively small so You would have practical problem with slightly imperfect mirrors absorbing the residual light very fast).
If that was Your own question, working principle of optical cable might also interesting to You (also trapped light idea, but both observer and candle can be rulled out of cosideration).