To me "sense of being one continuous self" sounds, well, New Age. Perhaps answering this may help me understand what you are talking about: Is it possible to have a "sense of being a discontinuous self"? If so, why might a person think his or her self is disrupted?

Another way of looking at this is that the way everybody talks about this subject, it sounds like if you ask anyone if their self is continuous, and they are functionally able to answer, they will always answer "yes." Without clear examples of disrupted self, it is hard to see that the notion of continuous self is meaningful except in a rhetorical or poetic way.