Originally, it wasn't 15 questions per day. It was 1500 questions per beta, with betas limited to 90 days - at the end of that time, you were expected to either graduate or close. 1500/90 is roughly 16.667 questions per day - I think we can agree that 15 is a cleaner-looking number. We've long ago transitioned to a model that looks at usage trends rather than hard numbers for graduation (and site-closing) purposes, but that metric still hangs around.
Where did 1500 questions come from? I don't know; I'll wager it was based on the beta numbers for previously successful sites, but Robert C can correct me if I'm wrong.
I will note that that sites which don't hit this during the private beta tend to be in rough shape. Some get by with less and go on to recover and do well, but... It's always worrying when less than half of the folks committed to a proposal manage to ask a single question.
Regardless, this generally isn't something you want to stress over unless folks are leaving and not coming back because there's nothing to do. As Robert wrote way back when,
As long as the questions and answers are of high quality, and people get answers to their questions, you shouldn’t worry about the site actually being closed.
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