American success against al Qaeda has had a lot to do with the experience of nations that have earlier destroyed similar Islamic terrorist organizations. In particular, the U.S. adopted the Israeli tactic of concentrating on the leadership and technicians. These are the skilled people required to plan a suicide bombing attack. This skilled crew must find a target that is not heavily guarded, build the bomb, recruit and train the bomber, and then get the bomber to the target for the attack. Without these "technicians", the attacks don't happen. That's how the Israelis stopped the Palestinian terror campaign cold after a few years. The Palestinians have been stymied for over five years now, and most have lost faith in the use of terror attacks on civilians.
Long term, the U.S. has found that you don't have to kill terrorist leaders to disable them. For example, when American troops drove al Qaeda and the Taliban out of Afghanistan in late 2001, they captured large quantities of records dealing with al Qaeda administration. This was revealing. The al Qaeda leadership was constantly being criticized by subordinates for stupid mistakes, while the leaders were constantly monitoring their people for stealing and malingering. The U.S. made sure a lot of this dirty linen was leaked, and eventually the media in Moslem nations began reporting on it. This paid off when al Qaeda in Iraq, despite vigorous objections within the organization, increased attacks that killed lots of civilians. This played a major role in al Qaeda going from an admired, to a despised, organization within the Islamic world. American intelligence leaked captured documents that made clear how uncaring the terrorist leaders were about these civilian deaths. The dead Moslem women and children were called "involuntary martyrs." This did not go over well in the Moslem world.
As al Qaeda popularity declined, so did donations from the Moslem world. This forced the terrorists to resort to crime to raise money. This was publicized, along with details via captured documents, by the Americans. As a result, Moslems began to regard Islamic terrorists as criminals, as well as thoughtless killers. This was in sharp contrast as al Qaeda propaganda that tried to portray them as selfless fighters for the protection of Islam. This made al Qaeda look like hypocrites.
The final blow came from the mouths of captured terrorists. Most of these men tended to speak freely once captured, and often complained about how hard life was as a terrorist. This was especially the case with suicide bombers, who often had to be persuaded to do the deed. Then there was the use of the mentally ill, very young children (10-12, or even younger) and grief stricken widows. In most Moslem countries, widows faced a hard life under any conditions, and suicide among them is common. The details of these recruiting methods were released, and by 2007, the Moslem media couldn't get enough of it. The callous treatment of young Saudi men, volunteering to "fight for Islam" in Iraq, was particularly effective in cutting off this source of manpower. The Saudi volunteers usually had no military training, and the Iraqi terrorist groups used most of them as suicide bombers, or in similar combat operations that were pretty much suicidal. Details of these policies were passed on to Saudi media, and parents began to regard a trip to Iraq, or even Afghanistan, as a form of murder (of innocent civilians as well as their sons).
This media campaign against al Qaeda was not, itself, publicized, but was carried out aggressively and discreetly. It worked, and it continues to work. Some things just don't survive the bright light of exposure.