Why did the Albigensian Crusade fail to eliminate Catharism immediately?

The Albigensian Crusade did not immediately eliminate Catharism primarily because the military campaign faced significant logistical and political challenges.12

The Crusade relied on northern French warriors who typically served for only 40 days to earn a Crusade indulgence. Consequently, commanders like Simon de Montfort were often left with only a skeleton force to defend captured territories after the seasonal recruits returned home. Furthermore, the movement was deeply entrenched in southern France, where it enjoyed the protection and tolerance of local secular lords, most notably Raymond VI of Toulouse.12

While the Crusade succeeded in establishing a new political framework of lords willing to cooperate with the Roman Catholic Church, it was not until the subsequent efforts of the Inquisition that the heresy was systematically and virtually eliminated within a century.12