I fail to see how giving a head coach 3 full years to succeed, which is very standard in the NFL, is refusing to admit he was wrong. If it continues past this year you might have a point.
Personally, I would have let DA go after his first year, but there are many good reasons nobody should hire me as an NFL GM and teams that fire coaches after one year have trouble getting good coaches and get a rep for being bad people to work for.
Loomis isn't perfect and has his issues, but I think a guy that did hire Payton, signed Brees, and guided this team through a highly successful 15 to 20 year period that included two NFC Championship appearances (should have been 3) and 1 Super Bowl win probably deserves to make more than one head coach hire post a HoF coach leaving before you throw him out. I think those 15 to 20 successful years have earned him that.