Having worked for an airline for a year and a half (before TSA -- you know, back when a non-passenger could go to the gate with a passenger), I might be able to help.
There are many different rules for fares. Some of them require an advance purchase. Some of them require a weekend stay. Some require booking a flight that isn't too full yet. (This is know as class of service -- more on this in a moment.) Most require a combination of the above. Also note that there are no fare rules requiring connections, to my knowledge -- the fare are priced for a specific route (like BOS-PIT), whether you have 0 connections or 10.
There are two cabins, of course: coach and first class. First class is always designated as an F class of service, since there are no discounted first-class fares. Coach, on the other hand, has many different designations. Generically (and full-fare), it is know as Y. Any seat in coach can be booked as a Y at any time. However, they also use other codes, such as H, L, K, V, and Q. Only so many seats are designated for each class of service. Once all the Q seats are booked, you can't get a Q fare any longer. (With the airline I worked for, Q was one of the lower-fare classes of service. Keep in mind that it's all coach class, but it's just the number of lower-fare seats designated.) A typical fare on the bottom pricing tier might require a Q seat, 21-day advance purchase, and a Saturday-night stay, and the ticket will be non-refundable and require a fee ($75 in 1999, but I think it's typically $100 now) for any changes. (And of course the new itinerary has to meet all the rules for the fare, or you have to pay the difference.) These restrictions are all designed to make the lower fares unattractive to businesses, who can and do pay $1000 for a one-way, fully-refundable, unrestricted, no-fee-for-changes coach ticket.
(Just as a side note: Apparently, the classes of service and what they mean are different for each airline. Googling on "fare basis" enlightened me on that. On another side note, a "fare basis" is a string of alphanumeric characters that determines the fare between two cities. A simple example might be QN21R. This means Q class, N is non-refundable, 21-day advance purchase, and R for round-trip. From there, they might get complicated. Y8 and F8 are often the designators for full-fare coach and first, respectively.)
Now, applying this to actual practice -- your situation -- what happened? My guess is that there simply weren't any seats left that were designated for a low-fare class of service on the non-stop flights since non-stops are more desirable than connections, causing them to sell out of the lower fares on the non-stops while leaving them still available on the connection.
Also note that I worked at the airport and not reservations, so I actually didn't deal with this stuff all that much. I was, however, one of the best people there at complicated ticket reissues.
And a nit-pick on terminology: I think you meant "non-stop flight" instead of "direct flight". All non-stop flights are direct flights, but not all direct flights are non-stop flights. The difference is as follows: A non-stop flight from A to B takes off at A, flies to B, and lands there without stopping anywhere else first. A direct flight, on the other hand, might land at C, D, and/or E in the interim, as long as it keeps the same flight number. For example, Southwest flight 7777 might originate in PHX, make a stop in STL, and then continue on to PHL, and it would be considered a direct flight between PHX-PHL. Or United flight 8888 might go PHX-LAX-BOS-DFW and be advertised as "direct service from PHX to DFW". (Think of the gate announcements saying things like, "Welcome to Blahblah Airlines flight 666 with non-stop service to Newark and continuing service to Providence.") Again, no big deal; I just wanted to point that out. And this information might also save you an enroute stop that you weren't expecting on a future flight. :-)
Of course, there are other explanations by analogy available. (This is actually taken from our reference system. There were a couple pieces of humor like this.)