Because the question does not specify a category of "organization" -- in effect, for-profit businesses; professional organizations; social organizations, etc. -- a general approach will be taken in responding.
Organizations can function only as well as a core group of members are willing and able to keep it operating. There is usually a hierarchy established within the organization, often involving a charter that specifies roles and responsibilities, such as "president," "vice president," "chairman" or "director," "treasurer," "secretary," and so on. Organizations experience catastrophic failure when these core individuals or divisions fail to execute their missions or responsibilities in an efficient manner. For example, an incompetent, lazy or dishonest Treasurer or accountant can undermine the entire enterprise by allowing the balance sheets to be corrupted or reflect improper data. An officer of the organization can lead the organization down the path to failure through poor decisionmaking. Dysfunctional communications within a large organization can also contribute to catastrophic failure of the organization.
In short, there are any number of factors that can cause an organization to fail. Without more specific information included in the question, however, a more detailed answer is not possible.