I think expecting a lower rate at any ONE particular time is a losing proposition. Fare sales happen at different times (although usually 1-3 months out), and the best ones are typically VERY short term. If you really want to catch a low fare, you have to set up an alert and buy it as quickly as possible when the fare sale happens.
In a similar situation, I find that the lowest rental car rates are USUALLY found less than a week out. But with rental cars, I always book as early as possible and monitor regularly. When a lower rate comes along, I book it and cancel my previous reservation. For our current trip, I had a two week Full Size for about $450. I was able to drop that to $326 a couple months out. I checked the day before our trip, and the lowest rate was about $1200. Conventional wisdom failed (big time) there, but the strategy of regular monitoring worked great.