The numbering of crusades is purely a scholarly device. Crusades can also be known by the pope who called them or by the papal bull of crusade. Papal bulls are always known by the first two or three words of the document.

There are five traditionally numbered crusades: the First in 1096 called by Urban II (no crusading bull), the Second in 1145 called by Eugene III with the bull Quantum praedecessores, the Third in 1187 by Gregory VIII with Audita tremendi, the Fourth by Innocent III in 1198 with Post miserabile, and the Fifth also by Innocent III with Quia maior in 1213 and Ad liberandem in 1215. Some scholars have numbered crusades beyond these five, but this is not a universal system.

There are also other crusades which are not numbered. For example, there was the Albigensian Crusade in the south of France from 1209 to 1229. These unnumbered crusades continued well into the early modern period, with papal bulls authorizing crusade in Spain, against the Ottomans, and against Protestants.

Why historians tend to stop numbering the crusades after 5 even though western occupation of the Levant would continue for another 70 years is an interesting question. For those who number up to 7, it's because their idea of "crusading" involves the attempt to retake Jerusalem, but several later bulls against the Ottomans seem to have similar goals. For these scholars, the fall of Acre marks the end of an era. For those who stop at 5, the answer is similar - the Fifth Crusade constituted the last great attempt to take Jerusalem. The failure of such a large, well organized, and well funded force to achieve even a few of its goals marked the futility of the struggle and the loss of the East.

More generally, I encourage you to look at how a historian defines the period in question when he or she writes a book or article. The bounds a person uses can tell you a lot about the subject of the book and the historian's own biases and understanding of the past. So too with the numbering of the Crusades.

A very important factor in the decline of Papal-sanctioned crusades was the end of the Papal Monarchy under Innocent IV (1243-1252). Innocent essentially preached a crusade against Holy Roman Emperor Fredrick II, and took on massive debt in order to finance the campaign, especially after the Battle of Parma (February 18, 1248). Innocent's actions caused the institution of the Papacy to lose a great deal of legitimacy and political capital, so much so that Louis IX of France actually went on not one but TWO crusades against Fatamid Egypt that the Pope specifically prohibited. Louis' first attempt (the 7th Crusade) resulted in his capture and the bankrupting of France, while the second attempt (the 8th Crusade) resulted in his death. Popes had essentially lost control of crusades as a tool for fighting Islam during the period following Innocent's death, and never regained that power.