To be correct, the dough should be punched-down at the first full rise. This is seen when you put the dough into a suitably sized container and allow it to rise until it begins to recede on its own. This is the best time to punch the dough. Punching the dough does a couple of things, it mixes the cooler outer portion of the dough with the warmer inner portion to help equilibrate the dough temperature; it also helps to prevent the development of a dry crust on the outer portion of the dough, and lastly, it mixes the more nutrient laden outer portion of the dough withthe more depleted inner portion to allow for better fermentation. (The outer dough portion is cooler so it doesn’t ferment as fast as the warmer, inner core, hence the outer portion has more remaining sugar available to support fermentation).
The reality is that we seldom put the dough into a suitably sized container to allow this to happen, hence, the more practical reason for punching the dough is to keep in in the container into which it was placed. More importantly than the number of times that the dough is punched, is the time between the last punch and taking the dough to the bench for scaling and balling. If you were to punch the dough and then wait 15 to 20-minutes before taking it to the bench you would probably find the dough to be somewhat tough and rubbery, however, if the last punch was an hour before you took the dough to the bench you would find that the dough was much more extensible and easy to work with, like with so many other things, when it comes to punching the dough, timing is everything.
Tom Lehmann/The Dough Doctor