Epiphany as a holiday has a very rich tradition but people speak less often of epiphany as a feeling. http://en.wikipedia.org/wiki/Epiphany_%28feeling%29
In pondering the nature of God or gods, philosophers and theologians often ask whether God is immanent in this world as in pantheism or transcendent, existing beyond this world in a separate dimension, or both, as in panentheism.
Somewhat in the same vein, the literary critics argue the question of whether a story is necessarily bound to the immediate contexts (historical, social, cultural, etc.) or if it could also exist beyond these contexts (across cultures and time in history) in a more timeless and universal sense. Another point they argue is whether the story belongs to the author or to the readers, or to both. http://en.wikipedia.org/wiki/New_Criticism.
It seems to me that, in writing, epiphany can accompany the climax of the story and the denouement that follows it or it could manifest (if subtly) much earlier, as a starting point of the unraveling of the hidden or the parallel narrative, in the mind of an observer-narrator, the dreamer within a dream.
Every dream (a story often with a very loose nonlinear plot created within the subconscious) that is powerful enough to break through the veil of the subconscious and transforms the dreamer like Scrooge's dream of the ghosts of Christams past, present and future can also be said to be an epiphany in the sense that it has a profound and lasting effect on the dreamer.
It seems to me that, if a story can be written without any signs of epiphany, good writing still plants a seed of epiphany in its readers. By showing and not telling, an author can plant enough clues in the reader's mind so that they eventually trigger sparks of insight that lead to an epiphany when a character finally comes alive to the reader or an elusive yet profound theme makes itself known.