I am afraid the answer is going to be “it depends”.
With low cost airlines at least, the increase is gradual and it's not uncommon to see markedly lower prices for flights at inconvenient times. So a ticket on such a flight might still be available at a given price a week out whereas similar tickets for a more attractive flight on the same day disappeared a few weeks before. In those conditions, it's very difficult to find any discontinuity or to formulate a reasonable rule of thumb.
I have the feeling full-service/legacy airlines tend to have steeper price changes when specific fares become unavailable so, with extensive data, it might be possible to say more. My completely anecdotal experience suggests that the most dramatic increases might happen two weeks before departure but I have seen exceptions as well (and of course one-way and return prices do not necessarily move in sync).
Some search engines like ITA Matrix, Momondo, or Adioso can show the best price available for a given route over one or two months so you could have a look at that casebut it still does not fully address the question (each look-up only covers one route and since you can only query the prices available on a given day, time-until-departure and calendar date are confused in the data).