I think this question is badly mis-framed. You need to just think in terms of revenue generators for your site, put them in, keep experimenting and tweaking, and at some point, if there is value and you are managing the business smartly, your revenues will start catching up to your costs and eventually overtake. The traffic at that point is irrelevant. Trying to guess that number in advance is pointless unless you are married to a single business model that you have no intention of changing (in which case the answer is easy: you'll probably NEVER be profitable).

You are getting caught up in traffic numbers but the fact that you are working with the Web instead of a physical business is actually irrelevant. You are asking when a business will turn cash-flow positive. You can't get there by turning on some magic switches at a certain traffic point. That's like saying you'll set up a coffee shop and give away free coffee until foot traffic hits a certain point. Revenue thinking starts from day 1 and grows from zero. You introduce each revenue experiment when you think you can get meaningful feedback to learn from and iterate. You turn off ones that aren't working, you improve ones that are.

And of course, that's the sideshow. Your main job is to get people to use whatever it is that you are producing in the first place, and get excited and happy about it. Do that right and the rest will take care of itself.