It's a quote by Katherine Anne Porter. Does it mean "past won't happen again", or something different?
What this quote means is that often people tend to think, or hope, that as time moves forward, we leave the past behind--particularly when there are painful things in our past we would prefer to forget. All the experiences of our lives make up the whole of who we are. Our past experiences impact, color, and shape our present and future experiences. We carry our past with us, we don't leave it back in time when the event happened, despite what many would hope. It is similar to William Faulkner's quote, "The past isn't dead, the past isn't even past." Events, triggers, reminders, bring our past right up into the present moment on a regular basis. This is neither good nor bad, it is simply what is. Knowing this can help us deal with how our past influences our now.
This is a quote from Porter's novel Ship of Fools, originally published in 1945.
This quote is attributed to Katherine Anne Porter. I'm not sure whether this was originally the title of a story. If so, there might be plot-related significance which is missed here. This answer simply considers the quote on its own merits.
The phrase leave the past behind means to not allow past events or decisions, etc to cripple your life in the present. For example, consider someone who made a poor decision 10 years ago that led to traumatic events, and as a consequence dithers over every decision today. They might be counselled to leave the past behind.
Suppose the person tried to do so, but then made another poor decision, leading to similar circumstances. They might then say that they tried, but the past is never where you think you left it. In this context, it means that the psychological baggage associated with that past incident was thought to have been dealt with, but has now resurfaced.
After finding a little context in a review at Language Matters: Essays on Language, Literature, and Translation edited by K.V. Tirumalesh, I think that Porter explains her aphorism:
Jenny: '“The past is never where you think you left it: you are not the same person you were yesterday.”
When you think back over past events of your life, it's not like picking up the thread of a novel you're reading again, after a gap of a few hours. It's the same you reading the novel, but it's a different you revisiting your past. You just read a bit more of the novel, but you re-interpret the past (perhaps subconsciously) in the light of intervening experiences.