At the beginning of a new golf season (April, here in Pennsylvania), I will clean out my bag and put in new balls that are Titleist, Callaway, and Bridgestone brands. I will continue to use a ball unless it either gets a ding on it (tree or cart path mark), or until it no longer performs by making too many double bogies. It then goes into my fall ball supply. (I always keep one or two of the discarded balls in my bag that I plop down when I have a long shot over water. No use putting a good ball in the lake.)
Back to the topic, after a round with Titleist, I will usually change to Bridgestone or Callaway, and continue to rotate the different brands, unless the Titleist (or whichever ball) round was exceptionally good. In that case, I will continue using Titleist until the streak ends or I lose the ball, then will go back to rotating different brands of balls.
Long about mid-November when the leaves start falling, I pull out my fall ball supply, and the better balls in the bag will return the following season. The reason for putting older balls in my bag is that I really don't want to lose a ball in a cluster of leaves, which happens at most courses here in Western Pennsylvania. Also, with the wet spring conditions here, I prefer using balls that are not new, but when April arrives I clean out my bag and start the procedure again.
There are some other instances that I have discarded an entire box of balls. In a round last year I tried a Srixon YELLOW ball and was 12 over par for the first 8 holes, I switched back to my Titleist white ball for the last ten holes and was 1 over par. (I knew it was the ball's fault.) After the round I gave the yellow balls to my wife.