I've only been following Newcastle since the beginning of the 06-07 season, but in that time there have been 7 managers, not including caretakers. That averages out to just shy of a year per manager. Granted, that includes dynamos like Roeder, Allardyce, and Kinnear.
Coming from an American sports background, coaches/managers generally get at least a couple of full seasons to show what they can do (subject to plenty of exceptions to prove the rule). It seems the tolerance level is a lot shorter in football (I'm not necessarily suggesting that's a bad thing or a good thing).
Assuming some baseline competence level, what is a reasonable period of time for a football manager to show what they can really do with a team?