As always, the question is how much time. That is far from an obvious answer.Here's another extremely obvious point: you make a hire, you give him and his assistants some support and some time.Sometimes, the obvious bears repeating ...
Let's look at a non coaching, non football example. Daniel Murphy of the Mets. If you looked at him, in the moment, at 3 separate points the past few month (prior to the postseason, after his monstrous nlds/cs, and after the World Series that saw a bad bat and costly fielding) you may come up with 3 very different valuations to his worth. This happens all of the time in professional sports where the guy you think your not/signing is a picture reflective of different points in time. That's why sometimes a guy is let go only to have a great season somewhere else, or sometimes re-signed for big money that future performances don't reflect.
As hard as it is to get this timing right with players, whom have a direct influence, imagine how hard it is with coaches whom have an indirect influence. It's harder to evaluate, but you still must evaluate and decide if the job being done is moving towards your stated goals.