I have noticed that ph has a tendency to creep back to where it started. If your ph is high out of the tap you will probably have your ph creeping up over time. If your ph is low out of the tap you will probably have your ph creeping down over time.
I'm not so sure I buy into this theory considering the chemistry. Of the sanitizers available (please correct if wrong), dichlor is the most benign re: pH with it's pH of 7.0. I use dichlor for sanitization and both dichlor or MPS (pH 3-4) for shocking. Out of the tap, pH is 7.5 for my water. After a water change, adding air and agitation causes the pH to jump to 8.0+. After initially adding dry acid to bring pH down to 7.8 or so, I find that pH will continue to drop, not rise. This makes sense considering that I am adding dichlor (pH 7.0) daily and either dichlor or MPS (pH 3-4) weekly to bi-weekly. After a while, soda ash is needed to bump pH back up. I would think that utilizing bromine would just exascerbate the problem since bromine is a bit more acidic than dichlor.