Another reason they don't lower ticket prices by much a long time before a flight is that there's too much statistical uncertainty in how well it will sell. As it gets closer the airline can make a better estimate of how many cheap tickets it wants to sell to fill seats that would otherwise be empty. Since few bargain hunters book more than a few months out, this doesn't impact (enough to notice) its ability to sell those discount tickets.

Another reason prices go up as a flight gets closer is that people who book at the last minute, like the people who book well in advance whom you mentioned, also absolutely have to be somewhere. In their case it's usually a business meeting that just came up. Since these passengers are spending the company's money, they're often less sensitive to pricing than a vacationer would be. Deep-discount tickets usually have an advance purchase restriction of 7 or 14 days for this reason. There's nothing magic about the numbers 7 and 14, but the're in the right area and people are used to them.

A fare going up "drastically" three months out is unusual. I suspect some event was announced for your destination city and people started to buy tickets to go there. Airline yield management software picks up unusual purchase patterns like this quickly and responds to them, but its response is based on imperfect knowledge. If it turns out the number of people going to whatever isn't enough to fill the planes, fares will come down again.

The best time to buy a ticket? Hard to say. For really popular routes, like Hawaii in January, probably as early as practical. For flights that will be nearly empty, I'd wait until 2-3 weeks before, perhaps even hoping for a last-minute Web special. For the normal kind of route, your 4-6 week guideline is probably about right, but there's no hard and fast rule.