What is your level of 'coaching' patience?
I think it depends on the situation. If you hire Urban Meyer, you have zero patience. Cut 5 games into the first season if need be. A young first time head coach you strongly believe in? You give him some slack but you need to see improvements where improvements can be made. As long as the coach can keep selling his vision to the team, and there is measured improvement in the areas he is emphasizing, I think you have to stick with him.
I thought Jim Haslett was a good coach for most of his tenure. He came in, won coach of the year, won a playoff game and then went on to struggle. The team gave him 5 years because that first year earned him some slack. I think the Saints handled him correctly.
DA inherited a team with no QB, but was otherwise stacked. He got his QB and the team is regressing. I think, given his track record, his leash is short. If the Saints fail to win a playoff game this year, he should be shown the door.