It's really a question about where travel takes us. I'm sure movement in itself is able to change who we are, and how we think about ourselves. A new context and a less stable routine are more than enough to unsettle how you live. But sometimes there's more to it than that. In rare instances, you feel more yourself in a new place - that is, more connected to a side of yourself that your old life doesn't bring out. It takes strangers or a new place to do it.
What happens, then, when you go back to the new place to find the feeling gone? Most often, the place hasn't changed, the people are the same, and you are just as convinced about who you really are. The implication is that an important part of what you experienced the first time round was simply novelty: you were new to them, and they were new to you. Take the surprise away, and suddenly what you thought was belonging was in fact just excitement - one of the least replicable sensations.
There is another possibility. You return, and feel the same sense of belonging, but this time embellished by the pleasure of recognition. This is where travel is at its best, I think, because the second journey is richer than the first, but only so because of the first. Without the first encounter, there couldn't be this kind of return. You would just be coming back.