I think what is at risk of being lost in this thread is that the objective at the very heart of hanging is to safely break down those limiting factors that stand in the way of growth and in order to do so you must maintain a very labile attitude as you proceed.
Fatigue is simply an indication that a limiting factor is breaking down, we then ride that fatigue as much as possible until it becomes dangerous to continue. It should then be expected that you might:
A. Have to raise your maximum weight to deal with the next limiting factor (which very may well include the new LF and the one you just conquered now working in concert)
B. Not be able to hang your maximum weight for a while because the next limiting factor(s) are not going to offer the same resistance as the one you just broke.
These are just two broadly noted examples of numerous possibilities. The bottom line is that everything expressed in this thread - on this entire forum, for that matter - is a great big generalization; this because hanging is a very personal experience that can and will vary greatly from one guy to the next.
The only and best way to deal with that is to get to know your own physiology really well and anticipate that you cannot anticipate anything.