The end of a well built argument which defends a true statement is saved into the argument itself.
Since the end of an argument is represented by its conclusion, it is confined to the boundaries of the premises and proofs brought into the argument.
Though such an end could be farther used for building other arguments, its real power of persuading is limited to the body of the argument it finishes.
Besides, the end of an argument supposes that the authority of the author of the argument comes to its end, too. Since his true conclusion is meant to establish an objective truth, the authority primarily belongs to that truth.
Meanwhile, the wrong argument with a false conclusion never ends into itself. Its premises and proofs are too weak for supporting the false conclusion in a repetitive way. They can support it at best only that time when it is issued. Otherwise, it will be discovered their falsely, too. Therefore, the lies are easily disentangled from the net of the premises and proves and become subject matters for preaching, where the arguments are only partially followed.
Because it can end into itself, a false argument never really ends. It delivers its conclusion to the liar who makes from it a personal feature of his authority. Thus, the lie will be alive as long its author and its followers are alive. It is easy to understand why false doctrines persist for centuries.