Please excuse my rambly nature. I am writing this later at night then I should, be, but I feel compelled to do so anyways.
While you could make many arguments, for the sake of this post, let's state that a system is a group of interconnected units, which all perform functions, or have functions performed on them. These units may be anything: Car parts, Computer pieces, Lego's, threads, musical notes, people, or anything else. During this post, I will write specifically about systems in which the main actors are human, but many of these concepts may well be applied elsewhere.
An ideal system will take some input, and create some output. This input and output may be anything, for example, an unruly mob to an ordered civilization (an ideal government), an uneducated human, to a knowledgeable one (an ideal school), and so on. As with physics, we will never reach a perfect ideal state, but we may approximate it as best we can, with imperfect but useful systems.
When it becomes so inefficient that it can no longer efficiently serve the purpose for which it was created, for any reason.
There are at least two common possibilities, or rather at least one possibility but two path's to reach it. Either a system is badly designed to start out with and collapses quickly, or the system becomes self serving, more focused on following the system for the systems sake, then for the accomplishment of the goal for which the system was established (For example, the education system caring about grades, as opposed to whether the students learn.)
Typically, it will be destroyed from the inside out, either by a well meaning, but short sighted member, or by a malicious and self serving member. In the first case, we have the example of standardized testing, resulting in a well meant, but destructive blow to the education system. In the second case, we have a corrupt authority being overly influenced by corporate lobbying, and therefore making decisions to further their own personal gain, rather than the gain of the society.
For our purposes, lets state that an authority is one who has control over some component of a system as defined above. Authority is neither good, nor bad. It just is, and always will be in some form.
An authority should not be respected for it's own sake, but rather for it's effectivity in preserving a useful system and it's ability to look beyond the system, see failure cases, and adjust the system to prevent these failure cases. This is the way to prevent/delay the first failure case that corrupts systems.
As with the previous question, authority should never be trusted in it's own right. Each authority must be judged from the perspective of both those above and below it in order to see that the power is not being abused. If the power is being abused, the authority must be removed and replaced as quickly as possible. This is the way to prevent the second failure case that corrupts systems.
If it has been shown that the authority can be both respected and trusted, then it may in the best interest of those under the authority to obey, at least within the domains within which it has earned respect and trust. However, if it has been shown that the authority can not be respected or trusted, don't those under the authority have a duty to disobey?